Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.599");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.4.b.f.599.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.192450i | 0.995360 | + | 0.0962250i | \(0.0306768\pi\) | ||||
−0.995360 | + | 0.0962250i | \(0.969323\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.136083 | ||||||||
\(7\) | 18.0000i | 0.971909i | 0.873984 | + | 0.485954i | \(0.161528\pi\) | ||||
−0.873984 | + | 0.485954i | \(0.838472\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 26.0000 | 0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.0000 | −0.877124 | −0.438562 | − | 0.898701i | \(-0.644512\pi\) | ||||
−0.438562 | + | 0.898701i | \(0.644512\pi\) | |||||||
\(12\) | − 4.00000i | − 0.0962250i | ||||||||
\(13\) | − 47.0000i | − 1.00273i | −0.865237 | − | 0.501364i | \(-0.832832\pi\) | ||||
0.865237 | − | 0.501364i | \(-0.167168\pi\) | |||||||
\(14\) | 36.0000 | 0.687243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − 20.0000i | − 0.285336i | −0.989771 | − | 0.142668i | \(-0.954432\pi\) | ||||
0.989771 | − | 0.142668i | \(-0.0455681\pi\) | |||||||
\(18\) | − 52.0000i | − 0.680918i | ||||||||
\(19\) | −36.0000 | −0.434682 | −0.217341 | − | 0.976096i | \(-0.569738\pi\) | ||||
−0.217341 | + | 0.976096i | \(0.569738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.0000 | −0.187044 | ||||||||
\(22\) | 64.0000i | 0.620220i | ||||||||
\(23\) | − 23.0000i | − 0.208514i | ||||||||
\(24\) | −8.00000 | −0.0680414 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −94.0000 | −0.709035 | ||||||||
\(27\) | 53.0000i | 0.377772i | ||||||||
\(28\) | − 72.0000i | − 0.485954i | ||||||||
\(29\) | 27.0000 | 0.172889 | 0.0864444 | − | 0.996257i | \(-0.472450\pi\) | ||||
0.0864444 | + | 0.996257i | \(0.472450\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −33.0000 | −0.191193 | −0.0955964 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955964 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | − 32.0000i | − 0.168803i | ||||||||
\(34\) | −40.0000 | −0.201763 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −104.000 | −0.481481 | ||||||||
\(37\) | − 56.0000i | − 0.248820i | −0.992231 | − | 0.124410i | \(-0.960296\pi\) | ||||
0.992231 | − | 0.124410i | \(-0.0397038\pi\) | |||||||
\(38\) | 72.0000i | 0.307367i | ||||||||
\(39\) | 47.0000 | 0.192975 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −157.000 | −0.598031 | −0.299016 | − | 0.954248i | \(-0.596658\pi\) | ||||
−0.299016 | + | 0.954248i | \(0.596658\pi\) | |||||||
\(42\) | 36.0000i | 0.132260i | ||||||||
\(43\) | 18.0000i | 0.0638366i | 0.999490 | + | 0.0319183i | \(0.0101616\pi\) | ||||
−0.999490 | + | 0.0319183i | \(0.989838\pi\) | |||||||
\(44\) | 128.000 | 0.438562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | − 65.0000i | − 0.201728i | −0.994900 | − | 0.100864i | \(-0.967839\pi\) | ||||
0.994900 | − | 0.100864i | \(-0.0321607\pi\) | |||||||
\(48\) | 16.0000i | 0.0481125i | ||||||||
\(49\) | 19.0000 | 0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.0000 | 0.0549129 | ||||||||
\(52\) | 188.000i | 0.501364i | ||||||||
\(53\) | − 14.0000i | − 0.0362839i | −0.999835 | − | 0.0181420i | \(-0.994225\pi\) | ||||
0.999835 | − | 0.0181420i | \(-0.00577508\pi\) | |||||||
\(54\) | 106.000 | 0.267125 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −144.000 | −0.343622 | ||||||||
\(57\) | − 36.0000i | − 0.0836547i | ||||||||
\(58\) | − 54.0000i | − 0.122251i | ||||||||
\(59\) | 744.000 | 1.64170 | 0.820852 | − | 0.571141i | \(-0.193499\pi\) | ||||
0.820852 | + | 0.571141i | \(0.193499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 552.000 | 1.15863 | 0.579314 | − | 0.815104i | \(-0.303320\pi\) | ||||
0.579314 | + | 0.815104i | \(0.303320\pi\) | |||||||
\(62\) | 66.0000i | 0.135194i | ||||||||
\(63\) | 468.000i | 0.935912i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −64.0000 | −0.119361 | ||||||||
\(67\) | 156.000i | 0.284454i | 0.989834 | + | 0.142227i | \(0.0454263\pi\) | ||||
−0.989834 | + | 0.142227i | \(0.954574\pi\) | |||||||
\(68\) | 80.0000i | 0.142668i | ||||||||
\(69\) | 23.0000 | 0.0401286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 699.000 | 1.16839 | 0.584197 | − | 0.811612i | \(-0.301409\pi\) | ||||
0.584197 | + | 0.811612i | \(0.301409\pi\) | |||||||
\(72\) | 208.000i | 0.340459i | ||||||||
\(73\) | − 609.000i | − 0.976412i | −0.872728 | − | 0.488206i | \(-0.837652\pi\) | ||||
0.872728 | − | 0.488206i | \(-0.162348\pi\) | |||||||
\(74\) | −112.000 | −0.175942 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 144.000 | 0.217341 | ||||||||
\(77\) | − 576.000i | − 0.852484i | ||||||||
\(78\) | − 94.0000i | − 0.136454i | ||||||||
\(79\) | 644.000 | 0.917160 | 0.458580 | − | 0.888653i | \(-0.348358\pi\) | ||||
0.458580 | + | 0.888653i | \(0.348358\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 314.000i | 0.422872i | ||||||||
\(83\) | 512.000i | 0.677100i | 0.940948 | + | 0.338550i | \(0.109936\pi\) | ||||
−0.940948 | + | 0.338550i | \(0.890064\pi\) | |||||||
\(84\) | 72.0000 | 0.0935220 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 36.0000 | 0.0451393 | ||||||||
\(87\) | 27.0000i | 0.0332725i | ||||||||
\(88\) | − 256.000i | − 0.310110i | ||||||||
\(89\) | 102.000 | 0.121483 | 0.0607415 | − | 0.998154i | \(-0.480653\pi\) | ||||
0.0607415 | + | 0.998154i | \(0.480653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 846.000 | 0.974559 | ||||||||
\(92\) | 92.0000i | 0.104257i | ||||||||
\(93\) | − 33.0000i | − 0.0367951i | ||||||||
\(94\) | −130.000 | −0.142643 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 32.0000 | 0.0340207 | ||||||||
\(97\) | − 578.000i | − 0.605021i | −0.953146 | − | 0.302510i | \(-0.902175\pi\) | ||||
0.953146 | − | 0.302510i | \(-0.0978247\pi\) | |||||||
\(98\) | − 38.0000i | − 0.0391692i | ||||||||
\(99\) | −832.000 | −0.844638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.00591111 | −0.00295556 | − | 0.999996i | \(-0.500941\pi\) | ||||
−0.00295556 | + | 0.999996i | \(0.500941\pi\) | |||||||
\(102\) | − 40.0000i | − 0.0388293i | ||||||||
\(103\) | − 160.000i | − 0.153061i | −0.997067 | − | 0.0765304i | \(-0.975616\pi\) | ||||
0.997067 | − | 0.0765304i | \(-0.0243842\pi\) | |||||||
\(104\) | 376.000 | 0.354518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.0000 | −0.0256566 | ||||||||
\(107\) | − 380.000i | − 0.343327i | −0.985156 | − | 0.171663i | \(-0.945086\pi\) | ||||
0.985156 | − | 0.171663i | \(-0.0549142\pi\) | |||||||
\(108\) | − 212.000i | − 0.188886i | ||||||||
\(109\) | −250.000 | −0.219685 | −0.109842 | − | 0.993949i | \(-0.535035\pi\) | ||||
−0.109842 | + | 0.993949i | \(0.535035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 56.0000 | 0.0478854 | ||||||||
\(112\) | 288.000i | 0.242977i | ||||||||
\(113\) | − 390.000i | − 0.324674i | −0.986735 | − | 0.162337i | \(-0.948097\pi\) | ||||
0.986735 | − | 0.162337i | \(-0.0519031\pi\) | |||||||
\(114\) | −72.0000 | −0.0591528 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −108.000 | −0.0864444 | ||||||||
\(117\) | − 1222.00i | − 0.965589i | ||||||||
\(118\) | − 1488.00i | − 1.16086i | ||||||||
\(119\) | 360.000 | 0.277321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −307.000 | −0.230654 | ||||||||
\(122\) | − 1104.00i | − 0.819274i | ||||||||
\(123\) | − 157.000i | − 0.115091i | ||||||||
\(124\) | 132.000 | 0.0955964 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 936.000 | 0.661790 | ||||||||
\(127\) | 769.000i | 0.537305i | 0.963237 | + | 0.268652i | \(0.0865783\pi\) | ||||
−0.963237 | + | 0.268652i | \(0.913422\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −18.0000 | −0.0122854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −213.000 | −0.142060 | −0.0710301 | − | 0.997474i | \(-0.522629\pi\) | ||||
−0.0710301 | + | 0.997474i | \(0.522629\pi\) | |||||||
\(132\) | 128.000i | 0.0844013i | ||||||||
\(133\) | − 648.000i | − 0.422472i | ||||||||
\(134\) | 312.000 | 0.201140 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 160.000 | 0.100882 | ||||||||
\(137\) | − 2836.00i | − 1.76858i | −0.466936 | − | 0.884291i | \(-0.654642\pi\) | ||||
0.466936 | − | 0.884291i | \(-0.345358\pi\) | |||||||
\(138\) | − 46.0000i | − 0.0283752i | ||||||||
\(139\) | 1631.00 | 0.995249 | 0.497625 | − | 0.867393i | \(-0.334206\pi\) | ||||
0.497625 | + | 0.867393i | \(0.334206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 65.0000 | 0.0388226 | ||||||||
\(142\) | − 1398.00i | − 0.826180i | ||||||||
\(143\) | 1504.00i | 0.879516i | ||||||||
\(144\) | 416.000 | 0.240741 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1218.00 | −0.690427 | ||||||||
\(147\) | 19.0000i | 0.0106605i | ||||||||
\(148\) | 224.000i | 0.124410i | ||||||||
\(149\) | 1966.00 | 1.08095 | 0.540473 | − | 0.841361i | \(-0.318245\pi\) | ||||
0.540473 | + | 0.841361i | \(0.318245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 35.0000 | 0.0188626 | 0.00943132 | − | 0.999956i | \(-0.496998\pi\) | ||||
0.00943132 | + | 0.999956i | \(0.496998\pi\) | |||||||
\(152\) | − 288.000i | − 0.153683i | ||||||||
\(153\) | − 520.000i | − 0.274768i | ||||||||
\(154\) | −1152.00 | −0.602797 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −188.000 | −0.0964875 | ||||||||
\(157\) | − 1702.00i | − 0.865187i | −0.901589 | − | 0.432594i | \(-0.857599\pi\) | ||||
0.901589 | − | 0.432594i | \(-0.142401\pi\) | |||||||
\(158\) | − 1288.00i | − 0.648530i | ||||||||
\(159\) | 14.0000 | 0.00698284 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 414.000 | 0.202657 | ||||||||
\(162\) | − 1298.00i | − 0.629509i | ||||||||
\(163\) | − 2045.00i | − 0.982680i | −0.870968 | − | 0.491340i | \(-0.836507\pi\) | ||||
0.870968 | − | 0.491340i | \(-0.163493\pi\) | |||||||
\(164\) | 628.000 | 0.299016 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1024.00 | 0.478782 | ||||||||
\(167\) | − 1016.00i | − 0.470781i | −0.971901 | − | 0.235391i | \(-0.924363\pi\) | ||||
0.971901 | − | 0.235391i | \(-0.0756369\pi\) | |||||||
\(168\) | − 144.000i | − 0.0661300i | ||||||||
\(169\) | −12.0000 | −0.00546199 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −936.000 | −0.418583 | ||||||||
\(172\) | − 72.0000i | − 0.0319183i | ||||||||
\(173\) | 598.000i | 0.262804i | 0.991329 | + | 0.131402i | \(0.0419479\pi\) | ||||
−0.991329 | + | 0.131402i | \(0.958052\pi\) | |||||||
\(174\) | 54.0000 | 0.0235272 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −512.000 | −0.219281 | ||||||||
\(177\) | 744.000i | 0.315946i | ||||||||
\(178\) | − 204.000i | − 0.0859014i | ||||||||
\(179\) | 4607.00 | 1.92371 | 0.961853 | − | 0.273567i | \(-0.0882036\pi\) | ||||
0.961853 | + | 0.273567i | \(0.0882036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1212.00 | −0.497720 | −0.248860 | − | 0.968540i | \(-0.580056\pi\) | ||||
−0.248860 | + | 0.968540i | \(0.580056\pi\) | |||||||
\(182\) | − 1692.00i | − 0.689117i | ||||||||
\(183\) | 552.000i | 0.222978i | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −66.0000 | −0.0260180 | ||||||||
\(187\) | 640.000i | 0.250275i | ||||||||
\(188\) | 260.000i | 0.100864i | ||||||||
\(189\) | −954.000 | −0.367160 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1058.00 | −0.400807 | −0.200404 | − | 0.979713i | \(-0.564225\pi\) | ||||
−0.200404 | + | 0.979713i | \(0.564225\pi\) | |||||||
\(192\) | − 64.0000i | − 0.0240563i | ||||||||
\(193\) | 1047.00i | 0.390491i | 0.980754 | + | 0.195245i | \(0.0625503\pi\) | ||||
−0.980754 | + | 0.195245i | \(0.937450\pi\) | |||||||
\(194\) | −1156.00 | −0.427814 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −76.0000 | −0.0276968 | ||||||||
\(197\) | − 251.000i | − 0.0907767i | −0.998969 | − | 0.0453883i | \(-0.985547\pi\) | ||||
0.998969 | − | 0.0453883i | \(-0.0144525\pi\) | |||||||
\(198\) | 1664.00i | 0.597249i | ||||||||
\(199\) | 3508.00 | 1.24963 | 0.624813 | − | 0.780775i | \(-0.285175\pi\) | ||||
0.624813 | + | 0.780775i | \(0.285175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −156.000 | −0.0547432 | ||||||||
\(202\) | 12.0000i | 0.00417979i | ||||||||
\(203\) | 486.000i | 0.168032i | ||||||||
\(204\) | −80.0000 | −0.0274565 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −320.000 | −0.108230 | ||||||||
\(207\) | − 598.000i | − 0.200792i | ||||||||
\(208\) | − 752.000i | − 0.250682i | ||||||||
\(209\) | 1152.00 | 0.381270 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3296.00 | −1.07538 | −0.537692 | − | 0.843141i | \(-0.680704\pi\) | ||||
−0.537692 | + | 0.843141i | \(0.680704\pi\) | |||||||
\(212\) | 56.0000i | 0.0181420i | ||||||||
\(213\) | 699.000i | 0.224858i | ||||||||
\(214\) | −760.000 | −0.242769 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −424.000 | −0.133563 | ||||||||
\(217\) | − 594.000i | − 0.185822i | ||||||||
\(218\) | 500.000i | 0.155341i | ||||||||
\(219\) | 609.000 | 0.187911 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −940.000 | −0.286114 | ||||||||
\(222\) | − 112.000i | − 0.0338601i | ||||||||
\(223\) | − 2720.00i | − 0.816792i | −0.912805 | − | 0.408396i | \(-0.866088\pi\) | ||||
0.912805 | − | 0.408396i | \(-0.133912\pi\) | |||||||
\(224\) | 576.000 | 0.171811 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −780.000 | −0.229579 | ||||||||
\(227\) | 4134.00i | 1.20874i | 0.796705 | + | 0.604368i | \(0.206574\pi\) | ||||
−0.796705 | + | 0.604368i | \(0.793426\pi\) | |||||||
\(228\) | 144.000i | 0.0418273i | ||||||||
\(229\) | 4510.00 | 1.30144 | 0.650719 | − | 0.759319i | \(-0.274468\pi\) | ||||
0.650719 | + | 0.759319i | \(0.274468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 576.000 | 0.164061 | ||||||||
\(232\) | 216.000i | 0.0611254i | ||||||||
\(233\) | − 5003.00i | − 1.40668i | −0.710852 | − | 0.703342i | \(-0.751690\pi\) | ||||
0.710852 | − | 0.703342i | \(-0.248310\pi\) | |||||||
\(234\) | −2444.00 | −0.682775 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2976.00 | −0.820852 | ||||||||
\(237\) | 644.000i | 0.176508i | ||||||||
\(238\) | − 720.000i | − 0.196095i | ||||||||
\(239\) | 6309.00 | 1.70751 | 0.853756 | − | 0.520674i | \(-0.174319\pi\) | ||||
0.853756 | + | 0.520674i | \(0.174319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3038.00 | 0.812012 | 0.406006 | − | 0.913871i | \(-0.366921\pi\) | ||||
0.406006 | + | 0.913871i | \(0.366921\pi\) | |||||||
\(242\) | 614.000i | 0.163097i | ||||||||
\(243\) | 2080.00i | 0.549103i | ||||||||
\(244\) | −2208.00 | −0.579314 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −314.000 | −0.0813817 | ||||||||
\(247\) | 1692.00i | 0.435868i | ||||||||
\(248\) | − 264.000i | − 0.0675968i | ||||||||
\(249\) | −512.000 | −0.130308 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1332.00 | −0.334961 | −0.167480 | − | 0.985875i | \(-0.553563\pi\) | ||||
−0.167480 | + | 0.985875i | \(0.553563\pi\) | |||||||
\(252\) | − 1872.00i | − 0.467956i | ||||||||
\(253\) | 736.000i | 0.182893i | ||||||||
\(254\) | 1538.00 | 0.379932 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 3301.00i | − 0.801209i | −0.916251 | − | 0.400605i | \(-0.868800\pi\) | ||||
0.916251 | − | 0.400605i | \(-0.131200\pi\) | |||||||
\(258\) | 36.0000i | 0.00868706i | ||||||||
\(259\) | 1008.00 | 0.241830 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 702.000 | 0.166485 | ||||||||
\(262\) | 426.000i | 0.100452i | ||||||||
\(263\) | 2072.00i | 0.485798i | 0.970052 | + | 0.242899i | \(0.0780984\pi\) | ||||
−0.970052 | + | 0.242899i | \(0.921902\pi\) | |||||||
\(264\) | 256.000 | 0.0596807 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1296.00 | −0.298733 | ||||||||
\(267\) | 102.000i | 0.0233794i | ||||||||
\(268\) | − 624.000i | − 0.142227i | ||||||||
\(269\) | −5721.00 | −1.29671 | −0.648356 | − | 0.761337i | \(-0.724543\pi\) | ||||
−0.648356 | + | 0.761337i | \(0.724543\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5900.00 | −1.32251 | −0.661254 | − | 0.750162i | \(-0.729975\pi\) | ||||
−0.661254 | + | 0.750162i | \(0.729975\pi\) | |||||||
\(272\) | − 320.000i | − 0.0713340i | ||||||||
\(273\) | 846.000i | 0.187554i | ||||||||
\(274\) | −5672.00 | −1.25058 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −92.0000 | −0.0200643 | ||||||||
\(277\) | − 6371.00i | − 1.38194i | −0.722885 | − | 0.690968i | \(-0.757185\pi\) | ||||
0.722885 | − | 0.690968i | \(-0.242815\pi\) | |||||||
\(278\) | − 3262.00i | − 0.703747i | ||||||||
\(279\) | −858.000 | −0.184112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3190.00 | 0.677222 | 0.338611 | − | 0.940926i | \(-0.390043\pi\) | ||||
0.338611 | + | 0.940926i | \(0.390043\pi\) | |||||||
\(282\) | − 130.000i | − 0.0274517i | ||||||||
\(283\) | − 4226.00i | − 0.887667i | −0.896109 | − | 0.443833i | \(-0.853618\pi\) | ||||
0.896109 | − | 0.443833i | \(-0.146382\pi\) | |||||||
\(284\) | −2796.00 | −0.584197 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3008.00 | 0.621912 | ||||||||
\(287\) | − 2826.00i | − 0.581232i | ||||||||
\(288\) | − 832.000i | − 0.170229i | ||||||||
\(289\) | 4513.00 | 0.918583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 578.000 | 0.116436 | ||||||||
\(292\) | 2436.00i | 0.488206i | ||||||||
\(293\) | 6048.00i | 1.20590i | 0.797780 | + | 0.602949i | \(0.206008\pi\) | ||||
−0.797780 | + | 0.602949i | \(0.793992\pi\) | |||||||
\(294\) | 38.0000 | 0.00753811 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 448.000 | 0.0879712 | ||||||||
\(297\) | − 1696.00i | − 0.331353i | ||||||||
\(298\) | − 3932.00i | − 0.764344i | ||||||||
\(299\) | −1081.00 | −0.209083 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −324.000 | −0.0620434 | ||||||||
\(302\) | − 70.0000i | − 0.0133379i | ||||||||
\(303\) | − 6.00000i | − 0.00113759i | ||||||||
\(304\) | −576.000 | −0.108671 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1040.00 | −0.194290 | ||||||||
\(307\) | − 8628.00i | − 1.60399i | −0.597328 | − | 0.801997i | \(-0.703771\pi\) | ||||
0.597328 | − | 0.801997i | \(-0.296229\pi\) | |||||||
\(308\) | 2304.00i | 0.426242i | ||||||||
\(309\) | 160.000 | 0.0294566 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8247.00 | 1.50368 | 0.751840 | − | 0.659346i | \(-0.229167\pi\) | ||||
0.751840 | + | 0.659346i | \(0.229167\pi\) | |||||||
\(312\) | 376.000i | 0.0682269i | ||||||||
\(313\) | 2620.00i | 0.473135i | 0.971615 | + | 0.236567i | \(0.0760224\pi\) | ||||
−0.971615 | + | 0.236567i | \(0.923978\pi\) | |||||||
\(314\) | −3404.00 | −0.611780 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2576.00 | −0.458580 | ||||||||
\(317\) | − 9906.00i | − 1.75513i | −0.479457 | − | 0.877565i | \(-0.659166\pi\) | ||||
0.479457 | − | 0.877565i | \(-0.340834\pi\) | |||||||
\(318\) | − 28.0000i | − 0.00493762i | ||||||||
\(319\) | −864.000 | −0.151645 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 380.000 | 0.0660733 | ||||||||
\(322\) | − 828.000i | − 0.143300i | ||||||||
\(323\) | 720.000i | 0.124031i | ||||||||
\(324\) | −2596.00 | −0.445130 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4090.00 | −0.694859 | ||||||||
\(327\) | − 250.000i | − 0.0422784i | ||||||||
\(328\) | − 1256.00i | − 0.211436i | ||||||||
\(329\) | 1170.00 | 0.196061 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8115.00 | −1.34756 | −0.673778 | − | 0.738934i | \(-0.735329\pi\) | ||||
−0.673778 | + | 0.738934i | \(0.735329\pi\) | |||||||
\(332\) | − 2048.00i | − 0.338550i | ||||||||
\(333\) | − 1456.00i | − 0.239605i | ||||||||
\(334\) | −2032.00 | −0.332892 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −288.000 | −0.0467610 | ||||||||
\(337\) | 7586.00i | 1.22622i | 0.789998 | + | 0.613109i | \(0.210082\pi\) | ||||
−0.789998 | + | 0.613109i | \(0.789918\pi\) | |||||||
\(338\) | 24.0000i | 0.00386221i | ||||||||
\(339\) | 390.000 | 0.0624835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1056.00 | 0.167700 | ||||||||
\(342\) | 1872.00i | 0.295983i | ||||||||
\(343\) | 6516.00i | 1.02575i | ||||||||
\(344\) | −144.000 | −0.0225697 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1196.00 | 0.185831 | ||||||||
\(347\) | − 1356.00i | − 0.209781i | −0.994484 | − | 0.104890i | \(-0.966551\pi\) | ||||
0.994484 | − | 0.104890i | \(-0.0334492\pi\) | |||||||
\(348\) | − 108.000i | − 0.0166362i | ||||||||
\(349\) | −6649.00 | −1.01981 | −0.509904 | − | 0.860231i | \(-0.670319\pi\) | ||||
−0.509904 | + | 0.860231i | \(0.670319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2491.00 | 0.378803 | ||||||||
\(352\) | 1024.00i | 0.155055i | ||||||||
\(353\) | 10691.0i | 1.61197i | 0.591938 | + | 0.805984i | \(0.298363\pi\) | ||||
−0.591938 | + | 0.805984i | \(0.701637\pi\) | |||||||
\(354\) | 1488.00 | 0.223408 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −408.000 | −0.0607415 | ||||||||
\(357\) | 360.000i | 0.0533704i | ||||||||
\(358\) | − 9214.00i | − 1.36027i | ||||||||
\(359\) | 6420.00 | 0.943829 | 0.471915 | − | 0.881644i | \(-0.343563\pi\) | ||||
0.471915 | + | 0.881644i | \(0.343563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5563.00 | −0.811051 | ||||||||
\(362\) | 2424.00i | 0.351941i | ||||||||
\(363\) | − 307.000i | − 0.0443893i | ||||||||
\(364\) | −3384.00 | −0.487280 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1104.00 | 0.157669 | ||||||||
\(367\) | 524.000i | 0.0745302i | 0.999305 | + | 0.0372651i | \(0.0118646\pi\) | ||||
−0.999305 | + | 0.0372651i | \(0.988135\pi\) | |||||||
\(368\) | − 368.000i | − 0.0521286i | ||||||||
\(369\) | −4082.00 | −0.575882 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 252.000 | 0.0352647 | ||||||||
\(372\) | 132.000i | 0.0183975i | ||||||||
\(373\) | 5566.00i | 0.772645i | 0.922364 | + | 0.386322i | \(0.126255\pi\) | ||||
−0.922364 | + | 0.386322i | \(0.873745\pi\) | |||||||
\(374\) | 1280.00 | 0.176971 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 520.000 | 0.0713217 | ||||||||
\(377\) | − 1269.00i | − 0.173360i | ||||||||
\(378\) | 1908.00i | 0.259622i | ||||||||
\(379\) | −2240.00 | −0.303591 | −0.151796 | − | 0.988412i | \(-0.548506\pi\) | ||||
−0.151796 | + | 0.988412i | \(0.548506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −769.000 | −0.103404 | ||||||||
\(382\) | 2116.00i | 0.283414i | ||||||||
\(383\) | 8778.00i | 1.17111i | 0.810633 | + | 0.585555i | \(0.199123\pi\) | ||||
−0.810633 | + | 0.585555i | \(0.800877\pi\) | |||||||
\(384\) | −128.000 | −0.0170103 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2094.00 | 0.276119 | ||||||||
\(387\) | 468.000i | 0.0614723i | ||||||||
\(388\) | 2312.00i | 0.302510i | ||||||||
\(389\) | −4056.00 | −0.528656 | −0.264328 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264328 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −460.000 | −0.0594967 | ||||||||
\(392\) | 152.000i | 0.0195846i | ||||||||
\(393\) | − 213.000i | − 0.0273395i | ||||||||
\(394\) | −502.000 | −0.0641888 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3328.00 | 0.422319 | ||||||||
\(397\) | 9151.00i | 1.15687i | 0.815730 | + | 0.578433i | \(0.196335\pi\) | ||||
−0.815730 | + | 0.578433i | \(0.803665\pi\) | |||||||
\(398\) | − 7016.00i | − 0.883619i | ||||||||
\(399\) | 648.000 | 0.0813047 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15930.0 | 1.98381 | 0.991903 | − | 0.126997i | \(-0.0405340\pi\) | ||||
0.991903 | + | 0.126997i | \(0.0405340\pi\) | |||||||
\(402\) | 312.000i | 0.0387093i | ||||||||
\(403\) | 1551.00i | 0.191714i | ||||||||
\(404\) | 24.0000 | 0.00295556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 972.000 | 0.118817 | ||||||||
\(407\) | 1792.00i | 0.218246i | ||||||||
\(408\) | 160.000i | 0.0194147i | ||||||||
\(409\) | 5891.00 | 0.712203 | 0.356102 | − | 0.934447i | \(-0.384106\pi\) | ||||
0.356102 | + | 0.934447i | \(0.384106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2836.00 | 0.340364 | ||||||||
\(412\) | 640.000i | 0.0765304i | ||||||||
\(413\) | 13392.0i | 1.59559i | ||||||||
\(414\) | −1196.00 | −0.141981 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1504.00 | −0.177259 | ||||||||
\(417\) | 1631.00i | 0.191536i | ||||||||
\(418\) | − 2304.00i | − 0.269599i | ||||||||
\(419\) | −15282.0 | −1.78180 | −0.890900 | − | 0.454199i | \(-0.849926\pi\) | ||||
−0.890900 | + | 0.454199i | \(0.849926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10934.0 | −1.26577 | −0.632887 | − | 0.774244i | \(-0.718130\pi\) | ||||
−0.632887 | + | 0.774244i | \(0.718130\pi\) | |||||||
\(422\) | 6592.00i | 0.760411i | ||||||||
\(423\) | − 1690.00i | − 0.194257i | ||||||||
\(424\) | 112.000 | 0.0128283 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1398.00 | 0.158998 | ||||||||
\(427\) | 9936.00i | 1.12608i | ||||||||
\(428\) | 1520.00i | 0.171663i | ||||||||
\(429\) | −1504.00 | −0.169263 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2794.00 | −0.312256 | −0.156128 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156128 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(432\) | 848.000i | 0.0944431i | ||||||||
\(433\) | − 15062.0i | − 1.67167i | −0.548980 | − | 0.835835i | \(-0.684984\pi\) | ||||
0.548980 | − | 0.835835i | \(-0.315016\pi\) | |||||||
\(434\) | −1188.00 | −0.131396 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1000.00 | 0.109842 | ||||||||
\(437\) | 828.000i | 0.0906376i | ||||||||
\(438\) | − 1218.00i | − 0.132873i | ||||||||
\(439\) | −261.000 | −0.0283755 | −0.0141878 | − | 0.999899i | \(-0.504516\pi\) | ||||
−0.0141878 | + | 0.999899i | \(0.504516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 494.000 | 0.0533420 | ||||||||
\(442\) | 1880.00i | 0.202313i | ||||||||
\(443\) | − 7083.00i | − 0.759647i | −0.925059 | − | 0.379823i | \(-0.875985\pi\) | ||||
0.925059 | − | 0.379823i | \(-0.124015\pi\) | |||||||
\(444\) | −224.000 | −0.0239427 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5440.00 | −0.577559 | ||||||||
\(447\) | 1966.00i | 0.208028i | ||||||||
\(448\) | − 1152.00i | − 0.121489i | ||||||||
\(449\) | 10370.0 | 1.08996 | 0.544978 | − | 0.838450i | \(-0.316538\pi\) | ||||
0.544978 | + | 0.838450i | \(0.316538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5024.00 | 0.524547 | ||||||||
\(452\) | 1560.00i | 0.162337i | ||||||||
\(453\) | 35.0000i | 0.00363012i | ||||||||
\(454\) | 8268.00 | 0.854706 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 288.000 | 0.0295764 | ||||||||
\(457\) | 10496.0i | 1.07436i | 0.843468 | + | 0.537180i | \(0.180510\pi\) | ||||
−0.843468 | + | 0.537180i | \(0.819490\pi\) | |||||||
\(458\) | − 9020.00i | − 0.920255i | ||||||||
\(459\) | 1060.00 | 0.107792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18021.0 | 1.82065 | 0.910327 | − | 0.413889i | \(-0.135830\pi\) | ||||
0.910327 | + | 0.413889i | \(0.135830\pi\) | |||||||
\(462\) | − 1152.00i | − 0.116008i | ||||||||
\(463\) | − 17188.0i | − 1.72526i | −0.505838 | − | 0.862629i | \(-0.668817\pi\) | ||||
0.505838 | − | 0.862629i | \(-0.331183\pi\) | |||||||
\(464\) | 432.000 | 0.0432222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10006.0 | −0.994676 | ||||||||
\(467\) | 15246.0i | 1.51071i | 0.655317 | + | 0.755354i | \(0.272535\pi\) | ||||
−0.655317 | + | 0.755354i | \(0.727465\pi\) | |||||||
\(468\) | 4888.00i | 0.482795i | ||||||||
\(469\) | −2808.00 | −0.276464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1702.00 | 0.166505 | ||||||||
\(472\) | 5952.00i | 0.580430i | ||||||||
\(473\) | − 576.000i | − 0.0559926i | ||||||||
\(474\) | 1288.00 | 0.124810 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1440.00 | −0.138660 | ||||||||
\(477\) | − 364.000i | − 0.0349401i | ||||||||
\(478\) | − 12618.0i | − 1.20739i | ||||||||
\(479\) | 8556.00 | 0.816145 | 0.408073 | − | 0.912949i | \(-0.366201\pi\) | ||||
0.408073 | + | 0.912949i | \(0.366201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2632.00 | −0.249499 | ||||||||
\(482\) | − 6076.00i | − 0.574179i | ||||||||
\(483\) | 414.000i | 0.0390014i | ||||||||
\(484\) | 1228.00 | 0.115327 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4160.00 | 0.388275 | ||||||||
\(487\) | 1805.00i | 0.167951i | 0.996468 | + | 0.0839757i | \(0.0267618\pi\) | ||||
−0.996468 | + | 0.0839757i | \(0.973238\pi\) | |||||||
\(488\) | 4416.00i | 0.409637i | ||||||||
\(489\) | 2045.00 | 0.189117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5245.00 | 0.482085 | 0.241042 | − | 0.970515i | \(-0.422511\pi\) | ||||
0.241042 | + | 0.970515i | \(0.422511\pi\) | |||||||
\(492\) | 628.000i | 0.0575456i | ||||||||
\(493\) | − 540.000i | − 0.0493314i | ||||||||
\(494\) | 3384.00 | 0.308205 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −528.000 | −0.0477982 | ||||||||
\(497\) | 12582.0i | 1.13557i | ||||||||
\(498\) | 1024.00i | 0.0921416i | ||||||||
\(499\) | −9027.00 | −0.809828 | −0.404914 | − | 0.914355i | \(-0.632698\pi\) | ||||
−0.404914 | + | 0.914355i | \(0.632698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1016.00 | 0.0906019 | ||||||||
\(502\) | 2664.00i | 0.236853i | ||||||||
\(503\) | 3522.00i | 0.312203i | 0.987741 | + | 0.156102i | \(0.0498927\pi\) | ||||
−0.987741 | + | 0.156102i | \(0.950107\pi\) | |||||||
\(504\) | −3744.00 | −0.330895 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1472.00 | 0.129325 | ||||||||
\(507\) | − 12.0000i | − 0.00105116i | ||||||||
\(508\) | − 3076.00i | − 0.268652i | ||||||||
\(509\) | −3949.00 | −0.343883 | −0.171941 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171941 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10962.0 | 0.948983 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | − 1908.00i | − 0.164211i | ||||||||
\(514\) | −6602.00 | −0.566540 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 72.0000 | 0.00614268 | ||||||||
\(517\) | 2080.00i | 0.176941i | ||||||||
\(518\) | − 2016.00i | − 0.171000i | ||||||||
\(519\) | −598.000 | −0.0505767 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3236.00 | 0.272115 | 0.136057 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136057 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(522\) | − 1404.00i | − 0.117723i | ||||||||
\(523\) | 12394.0i | 1.03624i | 0.855309 | + | 0.518118i | \(0.173367\pi\) | ||||
−0.855309 | + | 0.518118i | \(0.826633\pi\) | |||||||
\(524\) | 852.000 | 0.0710301 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4144.00 | 0.343511 | ||||||||
\(527\) | 660.000i | 0.0545542i | ||||||||
\(528\) | − 512.000i | − 0.0422006i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19344.0 | 1.58090 | ||||||||
\(532\) | 2592.00i | 0.211236i | ||||||||
\(533\) | 7379.00i | 0.599662i | ||||||||
\(534\) | 204.000 | 0.0165317 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1248.00 | −0.100570 | ||||||||
\(537\) | 4607.00i | 0.370217i | ||||||||
\(538\) | 11442.0i | 0.916914i | ||||||||
\(539\) | −608.000 | −0.0485870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7159.00 | −0.568927 | −0.284463 | − | 0.958687i | \(-0.591815\pi\) | ||||
−0.284463 | + | 0.958687i | \(0.591815\pi\) | |||||||
\(542\) | 11800.0i | 0.935154i | ||||||||
\(543\) | − 1212.00i | − 0.0957862i | ||||||||
\(544\) | −640.000 | −0.0504408 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1692.00 | 0.132621 | ||||||||
\(547\) | 19761.0i | 1.54464i | 0.635232 | + | 0.772321i | \(0.280904\pi\) | ||||
−0.635232 | + | 0.772321i | \(0.719096\pi\) | |||||||
\(548\) | 11344.0i | 0.884291i | ||||||||
\(549\) | 14352.0 | 1.11572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −972.000 | −0.0751517 | ||||||||
\(552\) | 184.000i | 0.0141876i | ||||||||
\(553\) | 11592.0i | 0.891396i | ||||||||
\(554\) | −12742.0 | −0.977176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6524.00 | −0.497625 | ||||||||
\(557\) | − 18010.0i | − 1.37003i | −0.728528 | − | 0.685016i | \(-0.759795\pi\) | ||||
0.728528 | − | 0.685016i | \(-0.240205\pi\) | |||||||
\(558\) | 1716.00i | 0.130187i | ||||||||
\(559\) | 846.000 | 0.0640107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −640.000 | −0.0481655 | ||||||||
\(562\) | − 6380.00i | − 0.478868i | ||||||||
\(563\) | − 2648.00i | − 0.198224i | −0.995076 | − | 0.0991118i | \(-0.968400\pi\) | ||||
0.995076 | − | 0.0991118i | \(-0.0316001\pi\) | |||||||
\(564\) | −260.000 | −0.0194113 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8452.00 | −0.627675 | ||||||||
\(567\) | 11682.0i | 0.865252i | ||||||||
\(568\) | 5592.00i | 0.413090i | ||||||||
\(569\) | 1566.00 | 0.115378 | 0.0576890 | − | 0.998335i | \(-0.481627\pi\) | ||||
0.0576890 | + | 0.998335i | \(0.481627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2864.00 | 0.209903 | 0.104952 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104952 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(572\) | − 6016.00i | − 0.439758i | ||||||||
\(573\) | − 1058.00i | − 0.0771354i | ||||||||
\(574\) | −5652.00 | −0.410993 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1664.00 | −0.120370 | ||||||||
\(577\) | 929.000i | 0.0670273i | 0.999438 | + | 0.0335137i | \(0.0106697\pi\) | ||||
−0.999438 | + | 0.0335137i | \(0.989330\pi\) | |||||||
\(578\) | − 9026.00i | − 0.649537i | ||||||||
\(579\) | −1047.00 | −0.0751500 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9216.00 | −0.658079 | ||||||||
\(582\) | − 1156.00i | − 0.0823329i | ||||||||
\(583\) | 448.000i | 0.0318255i | ||||||||
\(584\) | 4872.00 | 0.345214 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12096.0 | 0.852698 | ||||||||
\(587\) | 19499.0i | 1.37106i | 0.728046 | + | 0.685528i | \(0.240429\pi\) | ||||
−0.728046 | + | 0.685528i | \(0.759571\pi\) | |||||||
\(588\) | − 76.0000i | − 0.00533025i | ||||||||
\(589\) | 1188.00 | 0.0831081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 251.000 | 0.0174700 | ||||||||
\(592\) | − 896.000i | − 0.0622050i | ||||||||
\(593\) | 6570.00i | 0.454971i | 0.973782 | + | 0.227485i | \(0.0730504\pi\) | ||||
−0.973782 | + | 0.227485i | \(0.926950\pi\) | |||||||
\(594\) | −3392.00 | −0.234302 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7864.00 | −0.540473 | ||||||||
\(597\) | 3508.00i | 0.240491i | ||||||||
\(598\) | 2162.00i | 0.147844i | ||||||||
\(599\) | −1880.00 | −0.128238 | −0.0641191 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641191 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3701.00 | 0.251193 | 0.125596 | − | 0.992081i | \(-0.459916\pi\) | ||||
0.125596 | + | 0.992081i | \(0.459916\pi\) | |||||||
\(602\) | 648.000i | 0.0438713i | ||||||||
\(603\) | 4056.00i | 0.273919i | ||||||||
\(604\) | −140.000 | −0.00943132 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | −0.000804400 0 | ||||||||
\(607\) | 3080.00i | 0.205953i | 0.994684 | + | 0.102976i | \(0.0328366\pi\) | ||||
−0.994684 | + | 0.102976i | \(0.967163\pi\) | |||||||
\(608\) | 1152.00i | 0.0768417i | ||||||||
\(609\) | −486.000 | −0.0323378 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3055.00 | −0.202278 | ||||||||
\(612\) | 2080.00i | 0.137384i | ||||||||
\(613\) | 24004.0i | 1.58159i | 0.612083 | + | 0.790793i | \(0.290332\pi\) | ||||
−0.612083 | + | 0.790793i | \(0.709668\pi\) | |||||||
\(614\) | −17256.0 | −1.13419 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4608.00 | 0.301399 | ||||||||
\(617\) | − 780.000i | − 0.0508940i | −0.999676 | − | 0.0254470i | \(-0.991899\pi\) | ||||
0.999676 | − | 0.0254470i | \(-0.00810091\pi\) | |||||||
\(618\) | − 320.000i | − 0.0208289i | ||||||||
\(619\) | −21892.0 | −1.42151 | −0.710754 | − | 0.703440i | \(-0.751646\pi\) | ||||
−0.710754 | + | 0.703440i | \(0.751646\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1219.00 | 0.0787710 | ||||||||
\(622\) | − 16494.0i | − 1.06326i | ||||||||
\(623\) | 1836.00i | 0.118070i | ||||||||
\(624\) | 752.000 | 0.0482437 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5240.00 | 0.334557 | ||||||||
\(627\) | 1152.00i | 0.0733755i | ||||||||
\(628\) | 6808.00i | 0.432594i | ||||||||
\(629\) | −1120.00 | −0.0709973 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8050.00 | 0.507869 | 0.253935 | − | 0.967221i | \(-0.418275\pi\) | ||||
0.253935 | + | 0.967221i | \(0.418275\pi\) | |||||||
\(632\) | 5152.00i | 0.324265i | ||||||||
\(633\) | − 3296.00i | − 0.206958i | ||||||||
\(634\) | −19812.0 | −1.24106 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −56.0000 | −0.00349142 | ||||||||
\(637\) | − 893.000i | − 0.0555447i | ||||||||
\(638\) | 1728.00i | 0.107229i | ||||||||
\(639\) | 18174.0 | 1.12512 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25890.0 | −1.59531 | −0.797655 | − | 0.603114i | \(-0.793926\pi\) | ||||
−0.797655 | + | 0.603114i | \(0.793926\pi\) | |||||||
\(642\) | − 760.000i | − 0.0467209i | ||||||||
\(643\) | 4774.00i | 0.292797i | 0.989226 | + | 0.146398i | \(0.0467681\pi\) | ||||
−0.989226 | + | 0.146398i | \(0.953232\pi\) | |||||||
\(644\) | −1656.00 | −0.101328 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1440.00 | 0.0877029 | ||||||||
\(647\) | − 3349.00i | − 0.203497i | −0.994810 | − | 0.101749i | \(-0.967556\pi\) | ||||
0.994810 | − | 0.101749i | \(-0.0324438\pi\) | |||||||
\(648\) | 5192.00i | 0.314755i | ||||||||
\(649\) | −23808.0 | −1.43998 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 594.000 | 0.0357614 | ||||||||
\(652\) | 8180.00i | 0.491340i | ||||||||
\(653\) | 24813.0i | 1.48699i | 0.668739 | + | 0.743497i | \(0.266834\pi\) | ||||
−0.668739 | + | 0.743497i | \(0.733166\pi\) | |||||||
\(654\) | −500.000 | −0.0298953 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2512.00 | −0.149508 | ||||||||
\(657\) | − 15834.0i | − 0.940248i | ||||||||
\(658\) | − 2340.00i | − 0.138636i | ||||||||
\(659\) | −18180.0 | −1.07465 | −0.537323 | − | 0.843376i | \(-0.680565\pi\) | ||||
−0.537323 | + | 0.843376i | \(0.680565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29250.0 | −1.72117 | −0.860585 | − | 0.509307i | \(-0.829902\pi\) | ||||
−0.860585 | + | 0.509307i | \(0.829902\pi\) | |||||||
\(662\) | 16230.0i | 0.952865i | ||||||||
\(663\) | − 940.000i | − 0.0550627i | ||||||||
\(664\) | −4096.00 | −0.239391 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2912.00 | −0.169426 | ||||||||
\(667\) | − 621.000i | − 0.0360498i | ||||||||
\(668\) | 4064.00i | 0.235391i | ||||||||
\(669\) | 2720.00 | 0.157192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17664.0 | −1.01626 | ||||||||
\(672\) | 576.000i | 0.0330650i | ||||||||
\(673\) | − 23027.0i | − 1.31891i | −0.751745 | − | 0.659454i | \(-0.770787\pi\) | ||||
0.751745 | − | 0.659454i | \(-0.229213\pi\) | |||||||
\(674\) | 15172.0 | 0.867068 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.0000 | 0.00273100 | ||||||||
\(677\) | − 20106.0i | − 1.14141i | −0.821154 | − | 0.570706i | \(-0.806669\pi\) | ||||
0.821154 | − | 0.570706i | \(-0.193331\pi\) | |||||||
\(678\) | − 780.000i | − 0.0441825i | ||||||||
\(679\) | 10404.0 | 0.588025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4134.00 | −0.232621 | ||||||||
\(682\) | − 2112.00i | − 0.118582i | ||||||||
\(683\) | − 18745.0i | − 1.05016i | −0.851054 | − | 0.525079i | \(-0.824036\pi\) | ||||
0.851054 | − | 0.525079i | \(-0.175964\pi\) | |||||||
\(684\) | 3744.00 | 0.209292 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13032.0 | 0.725312 | ||||||||
\(687\) | 4510.00i | 0.250462i | ||||||||
\(688\) | 288.000i | 0.0159592i | ||||||||
\(689\) | −658.000 | −0.0363829 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24424.0 | 1.34462 | 0.672310 | − | 0.740270i | \(-0.265302\pi\) | ||||
0.672310 | + | 0.740270i | \(0.265302\pi\) | |||||||
\(692\) | − 2392.00i | − 0.131402i | ||||||||
\(693\) | − 14976.0i | − 0.820911i | ||||||||
\(694\) | −2712.00 | −0.148337 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −216.000 | −0.0117636 | ||||||||
\(697\) | 3140.00i | 0.170640i | ||||||||
\(698\) | 13298.0i | 0.721113i | ||||||||
\(699\) | 5003.00 | 0.270717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27278.0 | −1.46972 | −0.734862 | − | 0.678217i | \(-0.762753\pi\) | ||||
−0.734862 | + | 0.678217i | \(0.762753\pi\) | |||||||
\(702\) | − 4982.00i | − 0.267854i | ||||||||
\(703\) | 2016.00i | 0.108158i | ||||||||
\(704\) | 2048.00 | 0.109640 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21382.0 | 1.13983 | ||||||||
\(707\) | − 108.000i | − 0.00574506i | ||||||||
\(708\) | − 2976.00i | − 0.157973i | ||||||||
\(709\) | −12214.0 | −0.646977 | −0.323488 | − | 0.946232i | \(-0.604856\pi\) | ||||
−0.323488 | + | 0.946232i | \(0.604856\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16744.0 | 0.883191 | ||||||||
\(712\) | 816.000i | 0.0429507i | ||||||||
\(713\) | 759.000i | 0.0398664i | ||||||||
\(714\) | 720.000 | 0.0377385 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18428.0 | −0.961853 | ||||||||
\(717\) | 6309.00i | 0.328611i | ||||||||
\(718\) | − 12840.0i | − 0.667388i | ||||||||
\(719\) | −12932.0 | −0.670768 | −0.335384 | − | 0.942082i | \(-0.608866\pi\) | ||||
−0.335384 | + | 0.942082i | \(0.608866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2880.00 | 0.148761 | ||||||||
\(722\) | 11126.0i | 0.573500i | ||||||||
\(723\) | 3038.00i | 0.156272i | ||||||||
\(724\) | 4848.00 | 0.248860 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −614.000 | −0.0313880 | ||||||||
\(727\) | − 10046.0i | − 0.512497i | −0.966611 | − | 0.256249i | \(-0.917513\pi\) | ||||
0.966611 | − | 0.256249i | \(-0.0824866\pi\) | |||||||
\(728\) | 6768.00i | 0.344559i | ||||||||
\(729\) | 15443.0 | 0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 360.000 | 0.0182149 | ||||||||
\(732\) | − 2208.00i | − 0.111489i | ||||||||
\(733\) | − 5924.00i | − 0.298510i | −0.988799 | − | 0.149255i | \(-0.952312\pi\) | ||||
0.988799 | − | 0.149255i | \(-0.0476876\pi\) | |||||||
\(734\) | 1048.00 | 0.0527008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | − 4992.00i | − 0.249502i | ||||||||
\(738\) | 8164.00i | 0.407210i | ||||||||
\(739\) | −829.000 | −0.0412656 | −0.0206328 | − | 0.999787i | \(-0.506568\pi\) | ||||
−0.0206328 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1692.00 | −0.0838828 | ||||||||
\(742\) | − 504.000i | − 0.0249359i | ||||||||
\(743\) | 7072.00i | 0.349188i | 0.984641 | + | 0.174594i | \(0.0558613\pi\) | ||||
−0.984641 | + | 0.174594i | \(0.944139\pi\) | |||||||
\(744\) | 264.000 | 0.0130090 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11132.0 | 0.546342 | ||||||||
\(747\) | 13312.0i | 0.652022i | ||||||||
\(748\) | − 2560.00i | − 0.125138i | ||||||||
\(749\) | 6840.00 | 0.333682 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16234.0 | 0.788798 | 0.394399 | − | 0.918939i | \(-0.370953\pi\) | ||||
0.394399 | + | 0.918939i | \(0.370953\pi\) | |||||||
\(752\) | − 1040.00i | − 0.0504320i | ||||||||
\(753\) | − 1332.00i | − 0.0644632i | ||||||||
\(754\) | −2538.00 | −0.122584 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3816.00 | 0.183580 | ||||||||
\(757\) | − 9128.00i | − 0.438260i | −0.975696 | − | 0.219130i | \(-0.929678\pi\) | ||||
0.975696 | − | 0.219130i | \(-0.0703219\pi\) | |||||||
\(758\) | 4480.00i | 0.214671i | ||||||||
\(759\) | −736.000 | −0.0351978 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 165.000 | 0.00785972 | 0.00392986 | − | 0.999992i | \(-0.498749\pi\) | ||||
0.00392986 | + | 0.999992i | \(0.498749\pi\) | |||||||
\(762\) | 1538.00i | 0.0731179i | ||||||||
\(763\) | − 4500.00i | − 0.213514i | ||||||||
\(764\) | 4232.00 | 0.200404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17556.0 | 0.828099 | ||||||||
\(767\) | − 34968.0i | − 1.64618i | ||||||||
\(768\) | 256.000i | 0.0120281i | ||||||||
\(769\) | 20834.0 | 0.976974 | 0.488487 | − | 0.872571i | \(-0.337549\pi\) | ||||
0.488487 | + | 0.872571i | \(0.337549\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3301.00 | 0.154193 | ||||||||
\(772\) | − 4188.00i | − 0.195245i | ||||||||
\(773\) | − 31782.0i | − 1.47881i | −0.673262 | − | 0.739404i | \(-0.735107\pi\) | ||||
0.673262 | − | 0.739404i | \(-0.264893\pi\) | |||||||
\(774\) | 936.000 | 0.0434675 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4624.00 | 0.213907 | ||||||||
\(777\) | 1008.00i | 0.0465403i | ||||||||
\(778\) | 8112.00i | 0.373817i | ||||||||
\(779\) | 5652.00 | 0.259954 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22368.0 | −1.02483 | ||||||||
\(782\) | 920.000i | 0.0420705i | ||||||||
\(783\) | 1431.00i | 0.0653126i | ||||||||
\(784\) | 304.000 | 0.0138484 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −426.000 | −0.0193320 | ||||||||
\(787\) | − 33104.0i | − 1.49940i | −0.661776 | − | 0.749701i | \(-0.730197\pi\) | ||||
0.661776 | − | 0.749701i | \(-0.269803\pi\) | |||||||
\(788\) | 1004.00i | 0.0453883i | ||||||||
\(789\) | −2072.00 | −0.0934920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7020.00 | 0.315553 | ||||||||
\(792\) | − 6656.00i | − 0.298625i | ||||||||
\(793\) | − 25944.0i | − 1.16179i | ||||||||
\(794\) | 18302.0 | 0.818027 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14032.0 | −0.624813 | ||||||||
\(797\) | − 4736.00i | − 0.210486i | −0.994447 | − | 0.105243i | \(-0.966438\pi\) | ||||
0.994447 | − | 0.105243i | \(-0.0335621\pi\) | |||||||
\(798\) | − 1296.00i | − 0.0574911i | ||||||||
\(799\) | −1300.00 | −0.0575603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2652.00 | 0.116984 | ||||||||
\(802\) | − 31860.0i | − 1.40276i | ||||||||
\(803\) | 19488.0i | 0.856434i | ||||||||
\(804\) | 624.000 | 0.0273716 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3102.00 | 0.135562 | ||||||||
\(807\) | − 5721.00i | − 0.249552i | ||||||||
\(808\) | − 48.0000i | − 0.00208989i | ||||||||
\(809\) | 7470.00 | 0.324637 | 0.162318 | − | 0.986738i | \(-0.448103\pi\) | ||||
0.162318 | + | 0.986738i | \(0.448103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19919.0 | 0.862455 | 0.431227 | − | 0.902243i | \(-0.358081\pi\) | ||||
0.431227 | + | 0.902243i | \(0.358081\pi\) | |||||||
\(812\) | − 1944.00i | − 0.0840160i | ||||||||
\(813\) | − 5900.00i | − 0.254517i | ||||||||
\(814\) | 3584.00 | 0.154323 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 320.000 | 0.0137282 | ||||||||
\(817\) | − 648.000i | − 0.0277487i | ||||||||
\(818\) | − 11782.0i | − 0.503604i | ||||||||
\(819\) | 21996.0 | 0.938465 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22694.0 | −0.964709 | −0.482354 | − | 0.875976i | \(-0.660218\pi\) | ||||
−0.482354 | + | 0.875976i | \(0.660218\pi\) | |||||||
\(822\) | − 5672.00i | − 0.240674i | ||||||||
\(823\) | − 31907.0i | − 1.35141i | −0.737173 | − | 0.675704i | \(-0.763840\pi\) | ||||
0.737173 | − | 0.675704i | \(-0.236160\pi\) | |||||||
\(824\) | 1280.00 | 0.0541152 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26784.0 | 1.12825 | ||||||||
\(827\) | 15236.0i | 0.640638i | 0.947310 | + | 0.320319i | \(0.103790\pi\) | ||||
−0.947310 | + | 0.320319i | \(0.896210\pi\) | |||||||
\(828\) | 2392.00i | 0.100396i | ||||||||
\(829\) | −27286.0 | −1.14316 | −0.571581 | − | 0.820545i | \(-0.693670\pi\) | ||||
−0.571581 | + | 0.820545i | \(0.693670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6371.00 | 0.265954 | ||||||||
\(832\) | 3008.00i | 0.125341i | ||||||||
\(833\) | − 380.000i | − 0.0158058i | ||||||||
\(834\) | 3262.00 | 0.135436 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4608.00 | −0.190635 | ||||||||
\(837\) | − 1749.00i | − 0.0722273i | ||||||||
\(838\) | 30564.0i | 1.25992i | ||||||||
\(839\) | −23054.0 | −0.948644 | −0.474322 | − | 0.880351i | \(-0.657307\pi\) | ||||
−0.474322 | + | 0.880351i | \(0.657307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23660.0 | −0.970109 | ||||||||
\(842\) | 21868.0i | 0.895037i | ||||||||
\(843\) | 3190.00i | 0.130331i | ||||||||
\(844\) | 13184.0 | 0.537692 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3380.00 | −0.137360 | ||||||||
\(847\) | − 5526.00i | − 0.224174i | ||||||||
\(848\) | − 224.000i | − 0.00907098i | ||||||||
\(849\) | 4226.00 | 0.170832 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1288.00 | −0.0518826 | ||||||||
\(852\) | − 2796.00i | − 0.112429i | ||||||||
\(853\) | − 34506.0i | − 1.38507i | −0.721385 | − | 0.692534i | \(-0.756494\pi\) | ||||
0.721385 | − | 0.692534i | \(-0.243506\pi\) | |||||||
\(854\) | 19872.0 | 0.796260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3040.00 | 0.121384 | ||||||||
\(857\) | 22263.0i | 0.887386i | 0.896179 | + | 0.443693i | \(0.146332\pi\) | ||||
−0.896179 | + | 0.443693i | \(0.853668\pi\) | |||||||
\(858\) | 3008.00i | 0.119687i | ||||||||
\(859\) | −12851.0 | −0.510443 | −0.255221 | − | 0.966883i | \(-0.582148\pi\) | ||||
−0.255221 | + | 0.966883i | \(0.582148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2826.00 | 0.111858 | ||||||||
\(862\) | 5588.00i | 0.220798i | ||||||||
\(863\) | 15723.0i | 0.620182i | 0.950707 | + | 0.310091i | \(0.100360\pi\) | ||||
−0.950707 | + | 0.310091i | \(0.899640\pi\) | |||||||
\(864\) | 1696.00 | 0.0667814 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30124.0 | −1.18205 | ||||||||
\(867\) | 4513.00i | 0.176781i | ||||||||
\(868\) | 2376.00i | 0.0929109i | ||||||||
\(869\) | −20608.0 | −0.804463 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7332.00 | 0.285230 | ||||||||
\(872\) | − 2000.00i | − 0.0776704i | ||||||||
\(873\) | − 15028.0i | − 0.582613i | ||||||||
\(874\) | 1656.00 | 0.0640904 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2436.00 | −0.0939553 | ||||||||
\(877\) | 886.000i | 0.0341141i | 0.999855 | + | 0.0170571i | \(0.00542970\pi\) | ||||
−0.999855 | + | 0.0170571i | \(0.994570\pi\) | |||||||
\(878\) | 522.000i | 0.0200645i | ||||||||
\(879\) | −6048.00 | −0.232075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37120.0 | −1.41953 | −0.709764 | − | 0.704439i | \(-0.751199\pi\) | ||||
−0.709764 | + | 0.704439i | \(0.751199\pi\) | |||||||
\(882\) | − 988.000i | − 0.0377185i | ||||||||
\(883\) | − 7524.00i | − 0.286753i | −0.989668 | − | 0.143376i | \(-0.954204\pi\) | ||||
0.989668 | − | 0.143376i | \(-0.0457960\pi\) | |||||||
\(884\) | 3760.00 | 0.143057 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14166.0 | −0.537151 | ||||||||
\(887\) | − 9221.00i | − 0.349054i | −0.984652 | − | 0.174527i | \(-0.944160\pi\) | ||||
0.984652 | − | 0.174527i | \(-0.0558396\pi\) | |||||||
\(888\) | 448.000i | 0.0169301i | ||||||||
\(889\) | −13842.0 | −0.522211 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20768.0 | −0.780869 | ||||||||
\(892\) | 10880.0i | 0.408396i | ||||||||
\(893\) | 2340.00i | 0.0876877i | ||||||||
\(894\) | 3932.00 | 0.147098 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2304.00 | −0.0859054 | ||||||||
\(897\) | − 1081.00i | − 0.0402381i | ||||||||
\(898\) | − 20740.0i | − 0.770716i | ||||||||
\(899\) | −891.000 | −0.0330551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −280.000 | −0.0103531 | ||||||||
\(902\) | − 10048.0i | − 0.370911i | ||||||||
\(903\) | − 324.000i | − 0.0119402i | ||||||||
\(904\) | 3120.00 | 0.114789 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 70.0000 | 0.00256688 | ||||||||
\(907\) | − 29116.0i | − 1.06591i | −0.846143 | − | 0.532955i | \(-0.821081\pi\) | ||||
0.846143 | − | 0.532955i | \(-0.178919\pi\) | |||||||
\(908\) | − 16536.0i | − 0.604368i | ||||||||
\(909\) | −156.000 | −0.00569218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11440.0 | 0.416053 | 0.208026 | − | 0.978123i | \(-0.433296\pi\) | ||||
0.208026 | + | 0.978123i | \(0.433296\pi\) | |||||||
\(912\) | − 576.000i | − 0.0209137i | ||||||||
\(913\) | − 16384.0i | − 0.593901i | ||||||||
\(914\) | 20992.0 | 0.759687 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18040.0 | −0.650719 | ||||||||
\(917\) | − 3834.00i | − 0.138070i | ||||||||
\(918\) | − 2120.00i | − 0.0762205i | ||||||||
\(919\) | −2958.00 | −0.106176 | −0.0530878 | − | 0.998590i | \(-0.516906\pi\) | ||||
−0.0530878 | + | 0.998590i | \(0.516906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8628.00 | 0.308689 | ||||||||
\(922\) | − 36042.0i | − 1.28740i | ||||||||
\(923\) | − 32853.0i | − 1.17158i | ||||||||
\(924\) | −2304.00 | −0.0820303 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34376.0 | −1.21994 | ||||||||
\(927\) | − 4160.00i | − 0.147392i | ||||||||
\(928\) | − 864.000i | − 0.0305627i | ||||||||
\(929\) | −20907.0 | −0.738360 | −0.369180 | − | 0.929358i | \(-0.620361\pi\) | ||||
−0.369180 | + | 0.929358i | \(0.620361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −684.000 | −0.0240786 | ||||||||
\(932\) | 20012.0i | 0.703342i | ||||||||
\(933\) | 8247.00i | 0.289383i | ||||||||
\(934\) | 30492.0 | 1.06823 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9776.00 | 0.341387 | ||||||||
\(937\) | − 9748.00i | − 0.339865i | −0.985456 | − | 0.169932i | \(-0.945645\pi\) | ||||
0.985456 | − | 0.169932i | \(-0.0543549\pi\) | |||||||
\(938\) | 5616.00i | 0.195489i | ||||||||
\(939\) | −2620.00 | −0.0910548 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19624.0 | 0.679834 | 0.339917 | − | 0.940455i | \(-0.389601\pi\) | ||||
0.339917 | + | 0.940455i | \(0.389601\pi\) | |||||||
\(942\) | − 3404.00i | − 0.117737i | ||||||||
\(943\) | 3611.00i | 0.124698i | ||||||||
\(944\) | 11904.0 | 0.410426 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1152.00 | −0.0395928 | ||||||||
\(947\) | 41859.0i | 1.43636i | 0.695856 | + | 0.718181i | \(0.255025\pi\) | ||||
−0.695856 | + | 0.718181i | \(0.744975\pi\) | |||||||
\(948\) | − 2576.00i | − 0.0882538i | ||||||||
\(949\) | −28623.0 | −0.979075 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9906.00 | 0.337775 | ||||||||
\(952\) | 2880.00i | 0.0980476i | ||||||||
\(953\) | 29226.0i | 0.993413i | 0.867918 | + | 0.496707i | \(0.165458\pi\) | ||||
−0.867918 | + | 0.496707i | \(0.834542\pi\) | |||||||
\(954\) | −728.000 | −0.0247064 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −25236.0 | −0.853756 | ||||||||
\(957\) | − 864.000i | − 0.0291841i | ||||||||
\(958\) | − 17112.0i | − 0.577102i | ||||||||
\(959\) | 51048.0 | 1.71890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28702.0 | −0.963445 | ||||||||
\(962\) | 5264.00i | 0.176422i | ||||||||
\(963\) | − 9880.00i | − 0.330611i | ||||||||
\(964\) | −12152.0 | −0.406006 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 828.000 | 0.0275781 | ||||||||
\(967\) | 29849.0i | 0.992636i | 0.868141 | + | 0.496318i | \(0.165315\pi\) | ||||
−0.868141 | + | 0.496318i | \(0.834685\pi\) | |||||||
\(968\) | − 2456.00i | − 0.0815484i | ||||||||
\(969\) | −720.000 | −0.0238697 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9390.00 | −0.310339 | −0.155170 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155170 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(972\) | − 8320.00i | − 0.274552i | ||||||||
\(973\) | 29358.0i | 0.967291i | ||||||||
\(974\) | 3610.00 | 0.118760 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8832.00 | 0.289657 | ||||||||
\(977\) | − 33536.0i | − 1.09817i | −0.835767 | − | 0.549085i | \(-0.814976\pi\) | ||||
0.835767 | − | 0.549085i | \(-0.185024\pi\) | |||||||
\(978\) | − 4090.00i | − 0.133726i | ||||||||
\(979\) | −3264.00 | −0.106556 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6500.00 | −0.211548 | ||||||||
\(982\) | − 10490.0i | − 0.340885i | ||||||||
\(983\) | 28994.0i | 0.940758i | 0.882465 | + | 0.470379i | \(0.155883\pi\) | ||||
−0.882465 | + | 0.470379i | \(0.844117\pi\) | |||||||
\(984\) | 1256.00 | 0.0406909 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1080.00 | −0.0348826 | ||||||||
\(987\) | 1170.00i | 0.0377320i | ||||||||
\(988\) | − 6768.00i | − 0.217934i | ||||||||
\(989\) | 414.000 | 0.0133109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11272.0 | 0.361319 | 0.180659 | − | 0.983546i | \(-0.442177\pi\) | ||||
0.180659 | + | 0.983546i | \(0.442177\pi\) | |||||||
\(992\) | 1056.00i | 0.0337984i | ||||||||
\(993\) | − 8115.00i | − 0.259337i | ||||||||
\(994\) | 25164.0 | 0.802971 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2048.00 | 0.0651540 | ||||||||
\(997\) | − 61186.0i | − 1.94361i | −0.235784 | − | 0.971805i | \(-0.575766\pi\) | ||||
0.235784 | − | 0.971805i | \(-0.424234\pi\) | |||||||
\(998\) | 18054.0i | 0.572635i | ||||||||
\(999\) | 2968.00 | 0.0939974 |
(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 | 1150.4.b.f.599.1 | 2 | ||
5.2 | odd | 4 | 230.4.a.e.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 1150.4.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 1150.4.b.f.599.2 | 2 | ||
15.2 | even | 4 | 2070.4.a.e.1.1 | 1 | |||
20.7 | even | 4 | 1840.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.e.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
1150.4.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
1150.4.b.f.599.1 | 2 | 1.1 | even | 1 | trivial | ||
1150.4.b.f.599.2 | 2 | 5.4 | even | 2 | inner | ||
1840.4.a.d.1.1 | 1 | 20.7 | even | 4 | |||
2070.4.a.e.1.1 | 1 | 15.2 | even | 4 |