Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(829,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4140.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 829.20 | ||
Character | \(\chi\) | \(=\) | 4140.829 |
Dual form | 4140.2.f.d.829.19 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.79970 | + | 1.32706i | 0.804851 | + | 0.593477i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.476731i | 0.180187i | 0.995933 | + | 0.0900936i | \(0.0287166\pi\) | ||||
−0.995933 | + | 0.0900936i | \(0.971283\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39788 | 1.02450 | 0.512250 | − | 0.858837i | \(-0.328812\pi\) | ||||
0.512250 | + | 0.858837i | \(0.328812\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.28658i | − | 0.634184i | −0.948395 | − | 0.317092i | \(-0.897294\pi\) | ||
0.948395 | − | 0.317092i | \(-0.102706\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.61642i | 0.634576i | 0.948329 | + | 0.317288i | \(0.102772\pi\) | ||||
−0.948329 | + | 0.317288i | \(0.897228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.08093 | −1.16565 | −0.582823 | − | 0.812599i | \(-0.698052\pi\) | ||||
−0.582823 | + | 0.812599i | \(0.698052\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.47785 | + | 4.77661i | 0.295569 | + | 0.955321i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.19050 | 0.592460 | 0.296230 | − | 0.955117i | \(-0.404270\pi\) | ||||
0.296230 | + | 0.955117i | \(0.404270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.65066 | 0.655678 | 0.327839 | − | 0.944734i | \(-0.393680\pi\) | ||||
0.327839 | + | 0.944734i | \(0.393680\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.632648 | + | 0.857973i | −0.106937 | + | 0.145024i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.44368i | 1.38813i | 0.719911 | + | 0.694066i | \(0.244182\pi\) | ||||
−0.719911 | + | 0.694066i | \(0.755818\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.25142 | 0.820134 | 0.410067 | − | 0.912055i | \(-0.365505\pi\) | ||||
0.410067 | + | 0.912055i | \(0.365505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.269348i | 0.0410752i | 0.999789 | + | 0.0205376i | \(0.00653778\pi\) | ||||
−0.999789 | + | 0.0205376i | \(0.993462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.26483i | 1.20555i | 0.797911 | + | 0.602775i | \(0.205938\pi\) | ||||
−0.797911 | + | 0.602775i | \(0.794062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.77273 | 0.967533 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.77590i | − | 1.06810i | −0.845452 | − | 0.534051i | \(-0.820669\pi\) | ||
0.845452 | − | 0.534051i | \(-0.179331\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.11517 | + | 4.50918i | 0.824569 | + | 0.608017i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.35367 | −1.08756 | −0.543778 | − | 0.839229i | \(-0.683006\pi\) | ||||
−0.543778 | + | 0.839229i | \(0.683006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.45789 | 0.698811 | 0.349405 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349405 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.03442 | − | 4.11517i | 0.376374 | − | 0.510424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6.83523i | − | 0.835056i | −0.908664 | − | 0.417528i | \(-0.862897\pi\) | ||
0.908664 | − | 0.417528i | \(-0.137103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.28891 | 0.746357 | 0.373178 | − | 0.927760i | \(-0.378268\pi\) | ||||
0.373178 | + | 0.927760i | \(0.378268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.90839i | 0.574483i | 0.957858 | + | 0.287242i | \(0.0927383\pi\) | ||||
−0.957858 | + | 0.287242i | \(0.907262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.61987i | 0.184602i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.29907 | 1.04623 | 0.523113 | − | 0.852263i | \(-0.324770\pi\) | ||||
0.523113 | + | 0.852263i | \(0.324770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.19955i | 0.680489i | 0.940337 | + | 0.340244i | \(0.110510\pi\) | ||||
−0.940337 | + | 0.340244i | \(0.889490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.47214 | + | 4.70878i | −0.376607 | + | 0.510739i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.423349 | 0.0448749 | 0.0224374 | − | 0.999748i | \(-0.492857\pi\) | ||||
0.0224374 | + | 0.999748i | \(0.492857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.09008 | 0.114272 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.14415 | − | 6.74268i | −0.938170 | − | 0.691784i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.67355i | 0.880666i | 0.897835 | + | 0.440333i | \(0.145140\pi\) | ||||
−0.897835 | + | 0.440333i | \(0.854860\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.41335 | −0.936663 | −0.468331 | − | 0.883553i | \(-0.655145\pi\) | ||||
−0.468331 | + | 0.883553i | \(0.655145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.24556i | 0.516860i | 0.966030 | + | 0.258430i | \(0.0832052\pi\) | ||||
−0.966030 | + | 0.258430i | \(0.916795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.80032i | − | 0.174044i | −0.996206 | − | 0.0870220i | \(-0.972265\pi\) | ||
0.996206 | − | 0.0870220i | \(-0.0277350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.14276 | −0.205240 | −0.102620 | − | 0.994721i | \(-0.532722\pi\) | ||||
−0.102620 | + | 0.994721i | \(0.532722\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.6232i | − | 1.56378i | −0.623417 | − | 0.781889i | \(-0.714256\pi\) | ||
0.623417 | − | 0.781889i | \(-0.285744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.32706 | − | 1.79970i | 0.123749 | − | 0.167823i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.24733 | −0.114343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.545586 | 0.0495987 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.67914 | + | 10.5576i | −0.329072 | + | 0.944305i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.1594i | 0.901503i | 0.892649 | + | 0.450752i | \(0.148844\pi\) | ||||
−0.892649 | + | 0.450752i | \(0.851156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.12091 | −0.272675 | −0.136338 | − | 0.990662i | \(-0.543533\pi\) | ||||
−0.136338 | + | 0.990662i | \(0.543533\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.42224i | − | 0.210034i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.11542i | − | 0.0952972i | −0.998864 | − | 0.0476486i | \(-0.984827\pi\) | ||
0.998864 | − | 0.0476486i | \(-0.0151728\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.12777 | 0.0956564 | 0.0478282 | − | 0.998856i | \(-0.484770\pi\) | ||||
0.0478282 | + | 0.998856i | \(0.484770\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.76954i | − | 0.649721i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.74194 | + | 4.23397i | 0.476842 | + | 0.351612i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5098 | 1.10676 | 0.553382 | − | 0.832927i | \(-0.313337\pi\) | ||||
0.553382 | + | 0.832927i | \(0.313337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.39922 | −0.358004 | −0.179002 | − | 0.983849i | \(-0.557287\pi\) | ||||
−0.179002 | + | 0.983849i | \(0.557287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.57010 | + | 4.84463i | 0.527723 | + | 0.389130i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3773i | 1.62629i | 0.582063 | + | 0.813143i | \(0.302246\pi\) | ||||
−0.582063 | + | 0.813143i | \(0.697754\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.476731 | 0.0375716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.88927i | − | 0.226305i | −0.993578 | − | 0.113153i | \(-0.963905\pi\) | ||
0.993578 | − | 0.113153i | \(-0.0360949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.5218i | − | 0.968970i | −0.874800 | − | 0.484485i | \(-0.839007\pi\) | ||
0.874800 | − | 0.484485i | \(-0.160993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.77153 | 0.597810 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1150i | 1.07315i | 0.843854 | + | 0.536573i | \(0.180281\pi\) | ||||
−0.843854 | + | 0.536573i | \(0.819719\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.27716 | + | 0.704535i | −0.172137 | + | 0.0532578i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.879658 | −0.0657487 | −0.0328744 | − | 0.999459i | \(-0.510466\pi\) | ||||
−0.0328744 | + | 0.999459i | \(0.510466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29243 | −0.319054 | −0.159527 | − | 0.987194i | \(-0.550997\pi\) | ||||
−0.159527 | + | 0.987194i | \(0.550997\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.2052 | + | 15.1961i | −0.823825 | + | 1.11724i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.89029i | 0.650123i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5786 | −1.05487 | −0.527435 | − | 0.849595i | \(-0.676846\pi\) | ||||
−0.527435 | + | 0.849595i | \(0.676846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7282i | 1.56403i | 0.623258 | + | 0.782016i | \(0.285809\pi\) | ||||
−0.623258 | + | 0.782016i | \(0.714191\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.01527i | 0.428570i | 0.976771 | + | 0.214285i | \(0.0687422\pi\) | ||||
−0.976771 | + | 0.214285i | \(0.931258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.90913 | 0.560663 | 0.280332 | − | 0.959903i | \(-0.409556\pi\) | ||||
0.280332 | + | 0.959903i | \(0.409556\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.52101i | 0.106754i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.45099 | + | 6.96893i | 0.660086 | + | 0.486731i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.2644 | −1.19420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.5795 | 1.69213 | 0.846063 | − | 0.533083i | \(-0.178967\pi\) | ||||
0.846063 | + | 0.533083i | \(0.178967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.357440 | + | 0.484746i | −0.0243772 | + | 0.0330594i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.74038i | 0.118145i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.98267 | 0.402438 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35824i | 0.157920i | 0.996878 | + | 0.0789598i | \(0.0251599\pi\) | ||||
−0.996878 | + | 0.0789598i | \(0.974840\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 9.40161i | − | 0.624006i | −0.950081 | − | 0.312003i | \(-0.899000\pi\) | ||
0.950081 | − | 0.312003i | \(-0.101000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.37921 | 0.157223 | 0.0786114 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786114 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.6381i | − | 1.09000i | −0.838438 | − | 0.544998i | \(-0.816531\pi\) | ||
0.838438 | − | 0.544998i | \(-0.183469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9679 | + | 14.8742i | −0.715466 | + | 0.970287i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3942 | −1.12514 | −0.562569 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562569 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.6857 | 1.59015 | 0.795073 | − | 0.606514i | \(-0.207432\pi\) | ||||
0.795073 | + | 0.606514i | \(0.207432\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.1889 | + | 8.98779i | 0.778719 | + | 0.574209i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.6180i | 0.739234i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.29188 | 0.334021 | 0.167010 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167010 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.39788i | − | 0.213623i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2623i | 0.952037i | 0.879435 | + | 0.476019i | \(0.157920\pi\) | ||||
−0.879435 | + | 0.476019i | \(0.842080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.02536 | −0.250124 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.50790i | − | 0.462957i | −0.972840 | − | 0.231478i | \(-0.925644\pi\) | ||
0.972840 | − | 0.231478i | \(-0.0743563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3190 | − | 13.9943i | 0.633894 | − | 0.859662i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.76366 | 0.473359 | 0.236679 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236679 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50881 | −0.0916538 | −0.0458269 | − | 0.998949i | \(-0.514592\pi\) | ||||
−0.0458269 | + | 0.998949i | \(0.514592\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.02154 | + | 16.2303i | 0.302811 | + | 0.978726i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.93933i | − | 0.116523i | −0.998301 | − | 0.0582616i | \(-0.981444\pi\) | ||
0.998301 | − | 0.0582616i | \(-0.0185558\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.46254 | 0.266213 | 0.133107 | − | 0.991102i | \(-0.457505\pi\) | ||||
0.133107 | + | 0.991102i | \(0.457505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0910i | 1.07540i | 0.843137 | + | 0.537699i | \(0.180706\pi\) | ||||
−0.843137 | + | 0.537699i | \(0.819294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.50351i | 0.147778i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.1543 | 0.597313 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 15.2461i | − | 0.890687i | −0.895360 | − | 0.445344i | \(-0.853082\pi\) | ||
0.895360 | − | 0.445344i | \(-0.146918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0341 | − | 11.0858i | −0.875320 | − | 0.645439i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.28658 | −0.132237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.128406 | −0.00740122 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.82256 | + | 7.24292i | 0.562438 | + | 0.414728i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 32.4536i | − | 1.85223i | −0.377246 | − | 0.926113i | \(-0.623129\pi\) | ||
0.377246 | − | 0.926113i | \(-0.376871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.6744 | −1.45586 | −0.727930 | − | 0.685651i | \(-0.759518\pi\) | ||||
−0.727930 | + | 0.685651i | \(0.759518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.45980i | − | 0.195559i | −0.995208 | − | 0.0977797i | \(-0.968826\pi\) | ||
0.995208 | − | 0.0977797i | \(-0.0311741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.2692i | − | 0.745273i | −0.927977 | − | 0.372637i | \(-0.878454\pi\) | ||
0.927977 | − | 0.372637i | \(-0.121546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8409 | 0.606975 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.2939i | − | 0.739690i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9221 | − | 3.37922i | 0.605850 | − | 0.187445i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.94010 | −0.217225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.8901 | −1.91774 | −0.958868 | − | 0.283852i | \(-0.908387\pi\) | ||||
−0.958868 | + | 0.283852i | \(0.908387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.07073 | − | 12.3014i | 0.495587 | − | 0.672096i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89570i | 0.266686i | 0.991070 | + | 0.133343i | \(0.0425712\pi\) | ||||
−0.991070 | + | 0.133343i | \(0.957429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4045 | 0.671742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.56588i | 0.354524i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.43042i | 0.0767889i | 0.999263 | + | 0.0383945i | \(0.0122243\pi\) | ||||
−0.999263 | + | 0.0383945i | \(0.987776\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1336 | 0.542441 | 0.271220 | − | 0.962517i | \(-0.412573\pi\) | ||||
0.271220 | + | 0.962517i | \(0.412573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.70613i | − | 0.144033i | −0.997403 | − | 0.0720165i | \(-0.977057\pi\) | ||
0.997403 | − | 0.0720165i | \(-0.0229434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.3182 | + | 8.34574i | 0.600706 | + | 0.442946i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.33325 | −0.387034 | −0.193517 | − | 0.981097i | \(-0.561990\pi\) | ||||
−0.193517 | + | 0.981097i | \(0.561990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.81584 | 0.358729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.51370 | + | 8.83363i | −0.340943 | + | 0.462373i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.9825i | − | 1.35628i | −0.734935 | − | 0.678138i | \(-0.762787\pi\) | ||
0.734935 | − | 0.678138i | \(-0.237213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.70701 | 0.192458 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.8726i | 1.49497i | 0.664280 | + | 0.747484i | \(0.268738\pi\) | ||||
−0.664280 | + | 0.747484i | \(0.731262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.29534i | − | 0.375729i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.28834 | −0.220277 | −0.110139 | − | 0.993916i | \(-0.535129\pi\) | ||||
−0.110139 | + | 0.993916i | \(0.535129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 24.9529i | − | 1.27503i | −0.770436 | − | 0.637517i | \(-0.779962\pi\) | ||
0.770436 | − | 0.637517i | \(-0.220038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.14966 | + | 2.91529i | −0.109557 | + | 0.148577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.7851 | 1.25665 | 0.628327 | − | 0.777949i | \(-0.283740\pi\) | ||||
0.628327 | + | 0.777949i | \(0.283740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61642 | 0.132318 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.7355 | + | 12.3404i | 0.842056 | + | 0.620912i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.28792i | 0.415959i | 0.978133 | + | 0.207979i | \(0.0666887\pi\) | ||||
−0.978133 | + | 0.207979i | \(0.933311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.6623 | −0.532451 | −0.266225 | − | 0.963911i | \(-0.585777\pi\) | ||||
−0.266225 | + | 0.963911i | \(0.585777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.34754i | − | 0.415821i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.6906i | 1.42214i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.2848 | 1.34914 | 0.674572 | − | 0.738209i | \(-0.264328\pi\) | ||||
0.674572 | + | 0.738209i | \(0.264328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.98245i | − | 0.195964i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.22714 | + | 11.1573i | −0.403855 | + | 0.547692i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.69546 | 0.375948 | 0.187974 | − | 0.982174i | \(-0.439808\pi\) | ||||
0.187974 | + | 0.982174i | \(0.439808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.7126 | −1.64305 | −0.821526 | − | 0.570171i | \(-0.806877\pi\) | ||||
−0.821526 | + | 0.570171i | \(0.806877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.4976 | + | 3.86667i | −0.606224 | + | 0.187561i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.60194i | 0.125917i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.4448 | 1.12930 | 0.564649 | − | 0.825331i | \(-0.309011\pi\) | ||||
0.564649 | + | 0.825331i | \(0.309011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1795i | 1.25811i | 0.777361 | + | 0.629054i | \(0.216558\pi\) | ||||
−0.777361 | + | 0.629054i | \(0.783442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.08093i | 0.243054i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.0063 | −1.14576 | −0.572878 | − | 0.819641i | \(-0.694173\pi\) | ||||
−0.572878 | + | 0.819641i | \(0.694173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 37.5878i | − | 1.78585i | −0.450205 | − | 0.892925i | \(-0.648649\pi\) | ||
0.450205 | − | 0.892925i | \(-0.351351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.761901 | + | 0.561807i | 0.0361176 | + | 0.0266322i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5817 | 1.01850 | 0.509252 | − | 0.860617i | \(-0.329922\pi\) | ||||
0.509252 | + | 0.860617i | \(0.329922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8437 | 0.840227 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.96183 | + | 1.44660i | 0.0919719 | + | 0.0678178i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.0161i | 1.63798i | 0.573806 | + | 0.818991i | \(0.305466\pi\) | ||||
−0.573806 | + | 0.818991i | \(0.694534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1807 | 0.520738 | 0.260369 | − | 0.965509i | \(-0.416156\pi\) | ||||
0.260369 | + | 0.965509i | \(0.416156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.4818i | − | 1.04482i | −0.852695 | − | 0.522409i | \(-0.825033\pi\) | ||
0.852695 | − | 0.522409i | \(-0.174967\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.5559i | 1.92298i | 0.274841 | + | 0.961490i | \(0.411375\pi\) | ||||
−0.274841 | + | 0.961490i | \(0.588625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.25856 | 0.150467 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.915212i | 0.0420815i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.50883 | − | 24.2696i | −0.344529 | − | 1.11357i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6378 | 1.12573 | 0.562864 | − | 0.826549i | \(-0.309699\pi\) | ||||
0.562864 | + | 0.826549i | \(0.309699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.3072 | 0.880332 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.5103 | + | 15.6098i | −0.522655 | + | 0.708805i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.6802i | − | 1.43557i | −0.696267 | − | 0.717783i | \(-0.745157\pi\) | ||
0.696267 | − | 0.717783i | \(-0.254843\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7934 | −0.803006 | −0.401503 | − | 0.915858i | \(-0.631512\pi\) | ||||
−0.401503 | + | 0.915858i | \(0.631512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.34769i | 0.375961i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.99812i | 0.134484i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.1069 | −1.21347 | −0.606737 | − | 0.794903i | \(-0.707522\pi\) | ||||
−0.606737 | + | 0.794903i | \(0.707522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.86428i | 0.127712i | 0.997959 | + | 0.0638561i | \(0.0203399\pi\) | ||||
−0.997959 | + | 0.0638561i | \(0.979660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9412 | − | 12.4920i | −0.753874 | − | 0.555888i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7653 | 0.521490 | 0.260745 | − | 0.965408i | \(-0.416032\pi\) | ||||
0.260745 | + | 0.965408i | \(0.416032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.33998 | −0.103515 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.96115 | + | 9.44044i | −0.306745 | + | 0.415995i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.0829i | 1.23508i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.5122 | −0.548169 | −0.274084 | − | 0.961706i | \(-0.588375\pi\) | ||||
−0.274084 | + | 0.961706i | \(0.588375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8344i | 0.692391i | 0.938162 | + | 0.346195i | \(0.112527\pi\) | ||||
−0.938162 | + | 0.346195i | \(0.887473\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.55168i | 0.416078i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.0078i | − | 0.520116i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.38913 | − | 3.24005i | 0.103291 | − | 0.140079i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.0129 | 0.991236 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.1948 | 0.868240 | 0.434120 | − | 0.900855i | \(-0.357059\pi\) | ||||
0.434120 | + | 0.900855i | \(0.357059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.85633 | − | 2.84357i | −0.165187 | − | 0.121805i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.3218i | − | 1.46750i | −0.679422 | − | 0.733748i | \(-0.737769\pi\) | ||
0.679422 | − | 0.733748i | \(-0.262231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.2107 | −0.690599 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.43315i | 0.188517i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.9107i | 1.18262i | 0.806446 | + | 0.591308i | \(0.201388\pi\) | ||||
−0.806446 | + | 0.591308i | \(0.798612\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.615887 | 0.0260492 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13.3640i | − | 0.563227i | −0.959528 | − | 0.281614i | \(-0.909130\pi\) | ||
0.959528 | − | 0.281614i | \(-0.0908697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.0599 | − | 29.9168i | 0.928067 | − | 1.25861i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.1983 | −1.64328 | −0.821640 | − | 0.570007i | \(-0.806941\pi\) | ||||
−0.821640 | + | 0.570007i | \(0.806941\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.64904 | 0.236405 | 0.118202 | − | 0.992990i | \(-0.462287\pi\) | ||||
0.118202 | + | 0.992990i | \(0.462287\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.77661 | − | 1.47785i | 0.199198 | − | 0.0616305i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 8.82278i | − | 0.367297i | −0.982992 | − | 0.183649i | \(-0.941209\pi\) | ||
0.982992 | − | 0.183649i | \(-0.0587908\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.95551 | −0.122615 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.4216i | − | 1.09427i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.74701i | 0.278479i | 0.990259 | + | 0.139240i | \(0.0444658\pi\) | ||||
−0.990259 | + | 0.139240i | \(0.955534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.5488 | −0.764288 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.8242i | − | 0.773018i | −0.922286 | − | 0.386509i | \(-0.873681\pi\) | ||
0.922286 | − | 0.386509i | \(-0.126319\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.24482 | − | 1.65528i | −0.0920287 | − | 0.0678597i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.6986 | 0.845723 | 0.422861 | − | 0.906194i | \(-0.361026\pi\) | ||||
0.422861 | + | 0.906194i | \(0.361026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.83720 | −0.197314 | −0.0986568 | − | 0.995122i | \(-0.531455\pi\) | ||||
−0.0986568 | + | 0.995122i | \(0.531455\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.981891 | + | 0.724022i | 0.0399195 | + | 0.0294357i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.44486i | 0.342766i | 0.985204 | + | 0.171383i | \(0.0548236\pi\) | ||||
−0.985204 | + | 0.171383i | \(0.945176\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.8982 | 0.764540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.6765i | − | 0.996674i | −0.866984 | − | 0.498337i | \(-0.833944\pi\) | ||
0.866984 | − | 0.498337i | \(-0.166056\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.37233i | − | 0.256541i | −0.991739 | − | 0.128270i | \(-0.959058\pi\) | ||
0.991739 | − | 0.128270i | \(-0.0409425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6093 | −1.02932 | −0.514662 | − | 0.857393i | \(-0.672083\pi\) | ||||
−0.514662 | + | 0.857393i | \(0.672083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.201823i | 0.00808588i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.6319 | + | 14.1182i | −0.825278 | + | 0.564727i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.0922 | −0.880875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.2453 | −0.965192 | −0.482596 | − | 0.875843i | \(-0.660306\pi\) | ||||
−0.482596 | + | 0.875843i | \(0.660306\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4821 | + | 18.2839i | −0.535022 | + | 0.725575i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 15.4864i | − | 0.613594i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.3162 | 1.15792 | 0.578961 | − | 0.815355i | \(-0.303458\pi\) | ||||
0.578961 | + | 0.815355i | \(0.303458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.16350i | 0.0853200i | 0.999090 | + | 0.0426600i | \(0.0135832\pi\) | ||||
−0.999090 | + | 0.0426600i | \(0.986417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2320i | 1.62100i | 0.585740 | + | 0.810499i | \(0.300804\pi\) | ||||
−0.585740 | + | 0.810499i | \(0.699196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.3848 | −1.11420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.15816i | − | 0.0844555i | −0.999108 | − | 0.0422277i | \(-0.986554\pi\) | ||
0.999108 | − | 0.0422277i | \(-0.0134455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.61670 | − | 4.14162i | −0.219463 | − | 0.161827i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.6592 | −0.765812 | −0.382906 | − | 0.923787i | \(-0.625077\pi\) | ||||
−0.382906 | + | 0.923787i | \(0.625077\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8473 | −0.421911 | −0.210955 | − | 0.977496i | \(-0.567657\pi\) | ||||
−0.210955 | + | 0.977496i | \(0.567657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.21444 | − | 4.35930i | 0.124651 | − | 0.169046i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.19050i | − | 0.123537i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5452 | 0.715931 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2407i | 0.510393i | 0.966889 | + | 0.255197i | \(0.0821402\pi\) | ||||
−0.966889 | + | 0.255197i | \(0.917860\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 49.0637i | − | 1.88567i | −0.333257 | − | 0.942836i | \(-0.608148\pi\) | ||
0.333257 | − | 0.942836i | \(-0.391852\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.13495 | −0.158685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 21.8438i | − | 0.835831i | −0.908486 | − | 0.417915i | \(-0.862761\pi\) | ||
0.908486 | − | 0.417915i | \(-0.137239\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.48023 | − | 2.00743i | 0.0565567 | − | 0.0767000i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.7802 | −0.677373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.7696 | −0.599903 | −0.299952 | − | 0.953954i | \(-0.596971\pi\) | ||||
−0.299952 | + | 0.953954i | \(0.596971\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.02965 | + | 1.49662i | 0.0769891 | + | 0.0567699i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.7399i | 0.520437i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.6534 | −0.628991 | −0.314496 | − | 0.949259i | \(-0.601835\pi\) | ||||
−0.314496 | + | 0.949259i | \(0.601835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 42.9017i | − | 1.61807i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.48763i | − | 0.168775i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.7592 | −0.629405 | −0.314703 | − | 0.949190i | \(-0.601905\pi\) | ||||
−0.314703 | + | 0.949190i | \(0.601905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.65066i | − | 0.136718i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3106 | − | 13.9828i | 0.385595 | − | 0.522929i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8196 | 0.776440 | 0.388220 | − | 0.921567i | \(-0.373090\pi\) | ||||
0.388220 | + | 0.921567i | \(0.373090\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.50072 | −0.0931317 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.71506 | + | 15.2397i | 0.175113 | + | 0.565990i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.7272i | − | 1.02835i | −0.857687 | − | 0.514173i | \(-0.828099\pi\) | ||
0.857687 | − | 0.514173i | \(-0.171901\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.704728 | −0.0260653 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.1678i | − | 1.11427i | −0.830420 | − | 0.557137i | \(-0.811900\pi\) | ||
0.830420 | − | 0.557137i | \(-0.188100\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 23.2253i | − | 0.855515i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.443024 | −0.0162969 | −0.00814845 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00814845 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.3237i | − | 1.47933i | −0.672973 | − | 0.739667i | \(-0.734983\pi\) | ||
0.672973 | − | 0.739667i | \(-0.265017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.3136 | + | 17.9282i | 0.890780 | + | 0.656840i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.858270 | 0.0313605 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.10545 | −0.222791 | −0.111396 | − | 0.993776i | \(-0.535532\pi\) | ||||
−0.111396 | + | 0.993776i | \(0.535532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.91728 | − | 5.83801i | −0.288139 | − | 0.212467i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 52.4883i | − | 1.90772i | −0.300253 | − | 0.953860i | \(-0.597071\pi\) | ||
0.300253 | − | 0.953860i | \(-0.402929\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.4101 | −1.02987 | −0.514933 | − | 0.857230i | \(-0.672183\pi\) | ||||
−0.514933 | + | 0.857230i | \(0.672183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.02152i | − | 0.0369816i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1014i | 0.689710i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9501 | 1.00791 | 0.503953 | − | 0.863731i | \(-0.331878\pi\) | ||||
0.503953 | + | 0.863731i | \(0.331878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 37.8554i | − | 1.36156i | −0.732486 | − | 0.680782i | \(-0.761640\pi\) | ||
0.732486 | − | 0.680782i | \(-0.238360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.39512 | + | 17.4378i | 0.193798 | + | 0.626383i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.6821 | −0.955985 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3690 | 0.764642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27.0418 | + | 36.6731i | −0.965164 | + | 1.30892i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.4460i | 0.871405i | 0.900091 | + | 0.435702i | \(0.143500\pi\) | ||||
−0.900091 | + | 0.435702i | \(0.856500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.92479 | 0.281773 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.4799i | − | 0.443175i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.16201i | 0.218270i | 0.994027 | + | 0.109135i | \(0.0348080\pi\) | ||||
−0.994027 | + | 0.109135i | \(0.965192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.6243 | −0.765013 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.6781i | 0.588558i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.857973 | + | 0.632648i | 0.0302396 | + | 0.0222979i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.7345 | −1.60794 | −0.803970 | − | 0.594670i | \(-0.797283\pi\) | ||||
−0.803970 | + | 0.594670i | \(0.797283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0837 | −0.810578 | −0.405289 | − | 0.914189i | \(-0.632829\pi\) | ||||
−0.405289 | + | 0.914189i | \(0.632829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.83422 | − | 5.19983i | 0.134307 | − | 0.182142i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.36854i | − | 0.0478791i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.3412 | −1.23342 | −0.616708 | − | 0.787192i | \(-0.711534\pi\) | ||||
−0.616708 | + | 0.787192i | \(0.711534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 53.0658i | − | 1.84976i | −0.380261 | − | 0.924879i | \(-0.624166\pi\) | ||
0.380261 | − | 0.924879i | \(-0.375834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2618i | 0.565479i | 0.959197 | + | 0.282739i | \(0.0912431\pi\) | ||||
−0.959197 | + | 0.282739i | \(0.908757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.3521 | −0.567933 | −0.283966 | − | 0.958834i | \(-0.591650\pi\) | ||||
−0.283966 | + | 0.958834i | \(0.591650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.7203i | 0.613973i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.6172 | − | 22.5356i | 0.575061 | − | 0.779876i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.2765 | −1.07979 | −0.539893 | − | 0.841734i | \(-0.681535\pi\) | ||||
−0.539893 | + | 0.841734i | \(0.681535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.8207 | −0.648991 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9864 | + | 10.3133i | 0.481148 | + | 0.354787i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.260097i | 0.00893705i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.44368 | 0.289446 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47.9540i | − | 1.64191i | −0.570991 | − | 0.820956i | \(-0.693441\pi\) | ||
0.570991 | − | 0.820956i | \(-0.306559\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 32.4303i | − | 1.10780i | −0.832584 | − | 0.553899i | \(-0.813139\pi\) | ||
0.832584 | − | 0.553899i | \(-0.186861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0847 | 1.36767 | 0.683836 | − | 0.729636i | \(-0.260310\pi\) | ||||
0.683836 | + | 0.729636i | \(0.260310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 42.5831i | − | 1.44955i | −0.688988 | − | 0.724773i | \(-0.741945\pi\) | ||
0.688988 | − | 0.724773i | \(-0.258055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7314 | + | 25.4028i | −0.636888 | + | 0.863723i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.5971 | 1.07186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6293 | −0.529580 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.03316 | − | 1.75396i | −0.170152 | − | 0.0592947i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1323i | 0.612283i | 0.951986 | + | 0.306142i | \(0.0990381\pi\) | ||||
−0.951986 | + | 0.306142i | \(0.900962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.46099 | −0.183986 | −0.0919928 | − | 0.995760i | \(-0.529324\pi\) | ||||
−0.0919928 | + | 0.995760i | \(0.529324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.37316i | 0.248127i | 0.992274 | + | 0.124063i | \(0.0395926\pi\) | ||||
−0.992274 | + | 0.124063i | \(0.960407\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 0.364198i | − | 0.0122286i | −0.999981 | − | 0.00611429i | \(-0.998054\pi\) | ||
0.999981 | − | 0.00611429i | \(-0.00194625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.84331 | −0.162439 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 41.9930i | − | 1.40524i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.58312 | − | 1.16736i | −0.0529179 | − | 0.0390204i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.6474 | 0.388463 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.3450 | 0.677792 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.72508 | − | 5.69629i | −0.256790 | − | 0.189351i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.3106i | − | 0.807219i | −0.914931 | − | 0.403609i | \(-0.867755\pi\) | ||
0.914931 | − | 0.403609i | \(-0.132245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7464 | 0.587964 | 0.293982 | − | 0.955811i | \(-0.405019\pi\) | ||||
0.293982 | + | 0.955811i | \(0.405019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.0653i | 0.697160i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.48783i | − | 0.0491326i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.35677 | 0.0777428 | 0.0388714 | − | 0.999244i | \(-0.487624\pi\) | ||||
0.0388714 | + | 0.999244i | \(0.487624\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 14.3801i | − | 0.473328i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.3321 | + | 12.4785i | −1.32611 | + | 0.410289i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.3906 | −1.16113 | −0.580564 | − | 0.814215i | \(-0.697168\pi\) | ||||
−0.580564 | + | 0.814215i | \(0.697168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.4118 | −1.12780 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.7979 | + | 15.9999i | −0.385833 | + | 0.523252i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.87779i | 0.0940133i | 0.998895 | + | 0.0470067i | \(0.0149682\pi\) | ||||
−0.998895 | + | 0.0470067i | \(0.985032\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.4825 | 1.09150 | 0.545750 | − | 0.837948i | \(-0.316245\pi\) | ||||
0.545750 | + | 0.837948i | \(0.316245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.25142i | − | 0.171010i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 9.66496i | − | 0.314069i | −0.987593 | − | 0.157035i | \(-0.949807\pi\) | ||
0.987593 | − | 0.157035i | \(-0.0501934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2234 | 0.364328 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 21.4627i | − | 0.695245i | −0.937635 | − | 0.347623i | \(-0.886989\pi\) | ||
0.937635 | − | 0.347623i | \(-0.113011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.2371 | − | 19.3466i | −0.849013 | − | 0.626041i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.531757 | 0.0171713 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.6727 | −0.570086 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.8346 | + | 39.1043i | −0.928218 | + | 1.25881i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6289i | 0.341803i | 0.985288 | + | 0.170902i | \(0.0546680\pi\) | ||||
−0.985288 | + | 0.170902i | \(0.945332\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.6717 | −1.17685 | −0.588425 | − | 0.808552i | \(-0.700252\pi\) | ||||
−0.588425 | + | 0.808552i | \(0.700252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.537644i | 0.0172361i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.6532i | 1.07666i | 0.842734 | + | 0.538331i | \(0.180945\pi\) | ||||
−0.842734 | + | 0.538331i | \(0.819055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.43849 | 0.0459743 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 36.3596i | − | 1.15969i | −0.814727 | − | 0.579845i | \(-0.803113\pi\) | ||
0.814727 | − | 0.579845i | \(-0.196887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.98260 | + | 10.8257i | −0.254347 | + | 0.344935i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.269348 | 0.00856477 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.75294 | −0.309812 | −0.154906 | − | 0.987929i | \(-0.549508\pi\) | ||||
−0.154906 | + | 0.987929i | \(0.549508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2341 | + | 10.4959i | 0.451250 | + | 0.332741i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.13205i | − | 0.0358523i | −0.999839 | − | 0.0179261i | \(-0.994294\pi\) | ||
0.999839 | − | 0.0179261i | \(-0.00570637\pi\) | |||||||
\(998\) | 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 | 4140.2.f.d.829.20 | yes | 24 | |
3.2 | odd | 2 | inner | 4140.2.f.d.829.5 | ✓ | 24 | |
5.4 | even | 2 | inner | 4140.2.f.d.829.19 | yes | 24 | |
15.14 | odd | 2 | inner | 4140.2.f.d.829.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.f.d.829.5 | ✓ | 24 | 3.2 | odd | 2 | inner | |
4140.2.f.d.829.6 | yes | 24 | 15.14 | odd | 2 | inner | |
4140.2.f.d.829.19 | yes | 24 | 5.4 | even | 2 | inner | |
4140.2.f.d.829.20 | yes | 24 | 1.1 | even | 1 | trivial |