Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.3 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.d.1121.2 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | 0.988571 | + | 0.150756i | \(0.0481707\pi\) | ||||
−0.988571 | + | 0.150756i | \(0.951829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.26795 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73205i | 0.377964i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.19615i | 0.222120i | 0.993814 | + | 0.111060i | \(0.0354246\pi\) | ||||
−0.993814 | + | 0.111060i | \(0.964575\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73205 | −0.301511 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.00000i | − 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.535898i | − 0.0881012i | −0.999029 | − | 0.0440506i | \(-0.985974\pi\) | ||||
0.999029 | − | 0.0440506i | \(-0.0140263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73205 | 0.277350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.92820 | 0.457309 | 0.228654 | − | 0.973508i | \(-0.426567\pi\) | ||||
0.228654 | + | 0.973508i | \(0.426567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.92820 | 1.44818 | 0.724089 | − | 0.689707i | \(-0.242261\pi\) | ||||
0.724089 | + | 0.689707i | \(0.242261\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.92820i | − 0.550058i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.46410i | 0.201110i | 0.994932 | + | 0.100555i | \(0.0320618\pi\) | ||||
−0.994932 | + | 0.100555i | \(0.967938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.46410i | 1.23212i | 0.787699 | + | 0.616061i | \(0.211272\pi\) | ||||
−0.787699 | + | 0.616061i | \(0.788728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.46410i | 0.187459i | 0.995598 | + | 0.0937295i | \(0.0298789\pi\) | ||||
−0.995598 | + | 0.0937295i | \(0.970121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.46410i | − 0.667546i | −0.942653 | − | 0.333773i | \(-0.891678\pi\) | ||||
0.942653 | − | 0.333773i | \(-0.108322\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000i | 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.46410 | 0.885826 | 0.442913 | − | 0.896565i | \(-0.353945\pi\) | ||||
0.442913 | + | 0.896565i | \(0.353945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.73205i | − 0.200000i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26795 | 0.255164 | 0.127582 | − | 0.991828i | \(-0.459278\pi\) | ||||
0.127582 | + | 0.991828i | \(0.459278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.53590i | 0.936937i | 0.883480 | + | 0.468468i | \(0.155194\pi\) | ||||
−0.883480 | + | 0.468468i | \(0.844806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.26795i | 0.245994i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.07180 | −0.222120 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.53590 | 0.268805 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.00000i | − 0.104828i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.92820i | 0.718421i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.7321 | −1.80042 | −0.900208 | − | 0.435459i | \(-0.856586\pi\) | ||||
−0.900208 | + | 0.435459i | \(0.856586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.3923i | 1.43209i | 0.698055 | + | 0.716044i | \(0.254049\pi\) | ||||
−0.698055 | + | 0.716044i | \(0.745951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.92820 | 0.781189 | 0.390595 | − | 0.920563i | \(-0.372269\pi\) | ||||
0.390595 | + | 0.920563i | \(0.372269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.73205 | 0.169031 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.07180i | − 0.296962i | −0.988915 | − | 0.148481i | \(-0.952562\pi\) | ||||
0.988915 | − | 0.148481i | \(-0.0474383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.80385i | − 0.268560i | −0.990943 | − | 0.134280i | \(-0.957128\pi\) | ||||
0.990943 | − | 0.134280i | \(-0.0428721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.928203 | 0.0881012 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.92820 | 0.463606 | 0.231803 | − | 0.972763i | \(-0.425537\pi\) | ||||
0.231803 | + | 0.972763i | \(0.425537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.46410i | − 0.323029i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.26795 | −0.207903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0000 | 0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.07180i | 0.457309i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.392305 | 0.0348114 | 0.0174057 | − | 0.999849i | \(-0.494459\pi\) | ||||
0.0174057 | + | 0.999849i | \(0.494459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.3923i | − 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000i | 0.173422i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.19615 | 0.447214 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.3923 | −1.40049 | −0.700245 | − | 0.713903i | \(-0.746926\pi\) | ||||
−0.700245 | + | 0.713903i | \(0.746926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.9282i | 1.77511i | 0.460705 | + | 0.887554i | \(0.347597\pi\) | ||||
−0.460705 | + | 0.887554i | \(0.652403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.1962i | 1.44818i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.19615 | 0.0993351 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205i | 0.142857i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.8564i | 1.79055i | 0.445517 | + | 0.895273i | \(0.353020\pi\) | ||||
−0.445517 | + | 0.895273i | \(0.646980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.660254 | −0.0537307 | −0.0268654 | − | 0.999639i | \(-0.508553\pi\) | ||||
−0.0268654 | + | 0.999639i | \(0.508553\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.00000i | − 0.321288i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.92820i | − 0.393313i | −0.980472 | − | 0.196657i | \(-0.936992\pi\) | ||||
0.980472 | − | 0.196657i | \(-0.0630084\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.53590 | −0.201110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.4641i | − 0.897938i | −0.893547 | − | 0.448969i | \(-0.851791\pi\) | ||||
0.893547 | − | 0.448969i | \(-0.148209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.73205i | 0.134840i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.92820 | −0.613503 | −0.306751 | − | 0.951790i | \(-0.599242\pi\) | ||||
−0.306751 | + | 0.951790i | \(0.599242\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.00000i | 0.380143i | 0.981770 | + | 0.190071i | \(0.0608720\pi\) | ||||
−0.981770 | + | 0.190071i | \(0.939128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.3923 | −1.23212 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.07180i | 0.0801099i | 0.999197 | + | 0.0400549i | \(0.0127533\pi\) | ||||
−0.999197 | + | 0.0400549i | \(0.987247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4.39230i | − 0.326477i | −0.986587 | − | 0.163239i | \(-0.947806\pi\) | ||||
0.986587 | − | 0.163239i | \(-0.0521941\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.53590 | −0.187459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.535898 | −0.0394000 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.26795i | − 0.165849i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.19615i | 0.377964i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12436 | 0.587858 | 0.293929 | − | 0.955827i | \(-0.405037\pi\) | ||||
0.293929 | + | 0.955827i | \(0.405037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3205 | −1.67865 | −0.839323 | − | 0.543632i | \(-0.817049\pi\) | ||||
−0.839323 | + | 0.543632i | \(0.817049\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.73205i | − 0.124035i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8.00000i | − 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4641 | −1.23800 | −0.618999 | − | 0.785392i | \(-0.712461\pi\) | ||||
−0.618999 | + | 0.785392i | \(0.712461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.46410 | 0.667546 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.19615i | 0.0839534i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.92820i | − 0.204515i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000i | 0.0688428i | 0.999407 | + | 0.0344214i | \(0.0109588\pi\) | ||||
−0.999407 | + | 0.0344214i | \(0.989041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.9282i | 0.885826i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.46410 | 0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.92820i | 0.468165i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.26795i | 0.152559i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8564 | −1.26272 | −0.631359 | − | 0.775491i | \(-0.717503\pi\) | ||||
−0.631359 | + | 0.775491i | \(0.717503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.12436i | 0.539232i | 0.962968 | + | 0.269616i | \(0.0868968\pi\) | ||||
−0.962968 | + | 0.269616i | \(0.913103\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 8.00000i | − 0.528655i | −0.964433 | − | 0.264327i | \(-0.914850\pi\) | ||||
0.964433 | − | 0.264327i | \(-0.0851500\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.73205 | −0.113961 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9282 | 0.715930 | 0.357965 | − | 0.933735i | \(-0.383471\pi\) | ||||
0.357965 | + | 0.933735i | \(0.383471\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 9.92820i | − 0.647645i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.92820i | 0.255164i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.73205 | −0.112037 | −0.0560185 | − | 0.998430i | \(-0.517841\pi\) | ||||
−0.0560185 | + | 0.998430i | \(0.517841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.32051 | 0.600387 | 0.300193 | − | 0.953878i | \(-0.402949\pi\) | ||||
0.300193 | + | 0.953878i | \(0.402949\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.00000i | − 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.7846 | −0.936937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0718i | 0.698846i | 0.936965 | + | 0.349423i | \(0.113622\pi\) | ||||
−0.936965 | + | 0.349423i | \(0.886378\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.46410i | 0.217786i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.92820 | −0.245994 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.7846 | −1.29651 | −0.648254 | − | 0.761424i | \(-0.724501\pi\) | ||||
−0.648254 | + | 0.761424i | \(0.724501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.535898i | − 0.0332991i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4641 | 0.953557 | 0.476779 | − | 0.879023i | \(-0.341804\pi\) | ||||
0.476779 | + | 0.879023i | \(0.341804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.46410 | 0.0899390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.39230i | 0.268805i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 15.4641i | − 0.942863i | −0.881903 | − | 0.471431i | \(-0.843737\pi\) | ||||
0.881903 | − | 0.471431i | \(-0.156263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5359 | 0.882993 | 0.441496 | − | 0.897263i | \(-0.354448\pi\) | ||||
0.441496 | + | 0.897263i | \(0.354448\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.73205 | 0.104828 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.00000i | − 0.0603023i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 27.8564i | − 1.67373i | −0.547410 | − | 0.836865i | \(-0.684386\pi\) | ||||
0.547410 | − | 0.836865i | \(-0.315614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.7846 | 1.65749 | 0.828745 | − | 0.559626i | \(-0.189055\pi\) | ||||
0.828745 | + | 0.559626i | \(0.189055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1244i | 0.958493i | 0.877680 | + | 0.479247i | \(0.159090\pi\) | ||||
−0.877680 | + | 0.479247i | \(0.840910\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.46410i | 0.205196i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.92820 | 0.172846 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 30.7128i | − 1.80042i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 20.8564i | − 1.21844i | −0.793000 | − | 0.609222i | \(-0.791482\pi\) | ||||
0.793000 | − | 0.609222i | \(-0.208518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.46410 | 0.551021 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.19615 | −0.301511 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.46410i | − 0.200334i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.46410i | 0.199667i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.9282 | −1.43209 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.46410 | 0.0838342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5885i | 0.661388i | 0.943738 | + | 0.330694i | \(0.107283\pi\) | ||||
−0.943738 | + | 0.330694i | \(0.892717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.7321i | 0.781189i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.39230 | −0.362474 | −0.181237 | − | 0.983439i | \(-0.558010\pi\) | ||||
−0.181237 | + | 0.983439i | \(0.558010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.58846 | −0.202832 | −0.101416 | − | 0.994844i | \(-0.532337\pi\) | ||||
−0.101416 | + | 0.994844i | \(0.532337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 11.4641i | − 0.643888i | −0.946759 | − | 0.321944i | \(-0.895664\pi\) | ||||
0.946759 | − | 0.321944i | \(-0.104336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.19615 | −0.0669717 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.32051 | 0.296962 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.53590i | − 0.252384i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000i | 0.0554700i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.85641 | 0.268560 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.92820 | 0.547360 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.7846i | − 1.58215i | −0.611722 | − | 0.791073i | \(-0.709523\pi\) | ||||
0.611722 | − | 0.791073i | \(-0.290477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.46410 | −0.298536 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3923 | 0.566105 | 0.283052 | − | 0.959104i | \(-0.408653\pi\) | ||||
0.283052 | + | 0.959104i | \(0.408653\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.53590i | 0.463606i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000i | 0.216612i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | 0.323029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.00000i | − 0.107366i | −0.998558 | − | 0.0536828i | \(-0.982904\pi\) | ||||
0.998558 | − | 0.0536828i | \(-0.0170960\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.3205i | − 0.927146i | −0.886059 | − | 0.463573i | \(-0.846567\pi\) | ||||
0.886059 | − | 0.463573i | \(-0.153433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.19615 | 0.277350 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.19615 | 0.0636648 | 0.0318324 | − | 0.999493i | \(-0.489866\pi\) | ||||
0.0318324 | + | 0.999493i | \(0.489866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 7.46410i | − 0.396153i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.92820i | − 0.207903i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.6077 | 0.718187 | 0.359093 | − | 0.933302i | \(-0.383086\pi\) | ||||
0.359093 | + | 0.933302i | \(0.383086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.3205i | 0.909091i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.00000i | − 0.209370i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.85641 | −0.253502 | −0.126751 | − | 0.991935i | \(-0.540455\pi\) | ||||
−0.126751 | + | 0.991935i | \(0.540455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.46410i | 0.0760124i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.5359i | − 1.58109i | −0.612405 | − | 0.790544i | \(-0.709798\pi\) | ||||
0.612405 | − | 0.790544i | \(-0.290202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.73205 | −0.0894427 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.19615 | 0.0616050 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6.14359i | − 0.315575i | −0.987473 | − | 0.157788i | \(-0.949564\pi\) | ||||
0.987473 | − | 0.157788i | \(-0.0504361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.679492i | 0.0348114i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.14359 | 0.313923 | 0.156961 | − | 0.987605i | \(-0.449830\pi\) | ||||
0.156961 | + | 0.987605i | \(0.449830\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 31.0526i | − 1.57443i | −0.616680 | − | 0.787214i | \(-0.711523\pi\) | ||||
0.616680 | − | 0.787214i | \(-0.288477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.85641 | −0.397316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.26795i | − 0.114113i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 29.7846i | − 1.49485i | −0.664348 | − | 0.747423i | \(-0.731291\pi\) | ||||
0.664348 | − | 0.747423i | \(-0.268709\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.46410 | −0.173422 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.7846 | 1.18775 | 0.593873 | − | 0.804559i | \(-0.297598\pi\) | ||||
0.593873 | + | 0.804559i | \(0.297598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.00000i | − 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000i | 0.447214i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.535898 | 0.0265635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3205 | 1.64759 | 0.823797 | − | 0.566886i | \(-0.191852\pi\) | ||||
0.823797 | + | 0.566886i | \(0.191852\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 28.3923i | − 1.40049i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.46410i | 0.465698i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.53590 | 0.419011 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.2487 | −1.77511 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.1769i | 1.22997i | 0.788538 | + | 0.614986i | \(0.210839\pi\) | ||||
−0.788538 | + | 0.614986i | \(0.789161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 19.5885i | − 0.954683i | −0.878718 | − | 0.477341i | \(-0.841600\pi\) | ||||
0.878718 | − | 0.477341i | \(-0.158400\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.26795 | 0.110012 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.46410i | 0.0708528i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.73205i | 0.0836242i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.1962 | 1.59900 | 0.799501 | − | 0.600664i | \(-0.205097\pi\) | ||||
0.799501 | + | 0.600664i | \(0.205097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7846 | 0.614389 | 0.307195 | − | 0.951647i | \(-0.400610\pi\) | ||||
0.307195 | + | 0.951647i | \(0.400610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.07180i | 0.0993351i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.92820i | 0.331421i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.2487 | −1.34824 | −0.674119 | − | 0.738623i | \(-0.735476\pi\) | ||||
−0.674119 | + | 0.738623i | \(0.735476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 21.3205i | − 1.01297i | −0.862249 | − | 0.506484i | \(-0.830945\pi\) | ||||
0.862249 | − | 0.506484i | \(-0.169055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.53590i | − 0.120213i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.8564 | −1.79055 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.8564 | −1.07866 | −0.539330 | − | 0.842094i | \(-0.681323\pi\) | ||||
−0.539330 | + | 0.842094i | \(0.681323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92820i | 0.137884i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.14359i | − 0.0537307i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.0718 | 0.985697 | 0.492849 | − | 0.870115i | \(-0.335956\pi\) | ||||
0.492849 | + | 0.870115i | \(0.335956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 11.7846i | − 0.550058i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000i | 0.558896i | 0.960161 | + | 0.279448i | \(0.0901514\pi\) | ||||
−0.960161 | + | 0.279448i | \(0.909849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.2487 | −1.59167 | −0.795836 | − | 0.605512i | \(-0.792968\pi\) | ||||
−0.795836 | + | 0.605512i | \(0.792968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.92820 | 0.321288 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.7321i | 0.820541i | 0.911964 | + | 0.410271i | \(0.134566\pi\) | ||||
−0.911964 | + | 0.410271i | \(0.865434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5.46410i | − 0.252309i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.53590 | 0.393313 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.46410 | −0.159280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.00000i | − 0.0917663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.14359 | −0.189326 | −0.0946628 | − | 0.995509i | \(-0.530177\pi\) | ||||
−0.0946628 | + | 0.995509i | \(0.530177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.535898 | −0.0244349 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.00000i | 0.273009i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.7321i | 0.805171i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.7128 | −0.983901 | −0.491951 | − | 0.870623i | \(-0.663716\pi\) | ||||
−0.491951 | + | 0.870623i | \(0.663716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.8564 | 0.897938 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 19.7846i | − 0.892867i | −0.894817 | − | 0.446433i | \(-0.852694\pi\) | ||||
0.894817 | − | 0.446433i | \(-0.147306\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.71281i | − 0.122179i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.46410 | 0.334811 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.78461i | 0.169422i | 0.996406 | + | 0.0847112i | \(0.0269968\pi\) | ||||
−0.996406 | + | 0.0847112i | \(0.973003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 13.7321i | − 0.613503i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.78461 | 0.168747 | 0.0843737 | − | 0.996434i | \(-0.473111\pi\) | ||||
0.0843737 | + | 0.996434i | \(0.473111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.3923 | 0.640449 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.7846i | 0.923077i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 31.4641i | − 1.39462i | −0.716769 | − | 0.697311i | \(-0.754380\pi\) | ||||
0.716769 | − | 0.697311i | \(-0.245620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.3923 | −0.458831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 7.92820i | − 0.349358i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.92820i | 0.436642i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.66025 | −0.380143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7846 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22.3923i | − 0.979147i | −0.871962 | − | 0.489574i | \(-0.837152\pi\) | ||||
0.871962 | − | 0.489574i | \(-0.162848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.73205i | − 0.0755929i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.07180 | −0.395174 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 2.92820i | − 0.126835i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.07180 | −0.132805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.85641 | −0.0801099 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 15.0526i | − 0.647160i | −0.946201 | − | 0.323580i | \(-0.895114\pi\) | ||||
0.946201 | − | 0.323580i | \(-0.104886\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.60770 | 0.326477 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.80385 | −0.120104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.1769i | 1.24751i | 0.781618 | + | 0.623757i | \(0.214395\pi\) | ||||
−0.781618 | + | 0.623757i | \(0.785605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.39230 | −0.101916 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.26795 | 0.0964430 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 0.928203i | − 0.0394000i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.78461i | 0.202730i | 0.994849 | + | 0.101365i | \(0.0323211\pi\) | ||||
−0.994849 | + | 0.101365i | \(0.967679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46410 | 0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.92820 | 0.165849 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.32051i | 0.224233i | 0.993695 | + | 0.112116i | \(0.0357629\pi\) | ||||
−0.993695 | + | 0.112116i | \(0.964237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.92820i | − 0.207331i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.00000 | −0.377964 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.6410 | −1.53607 | −0.768036 | − | 0.640407i | \(-0.778766\pi\) | ||||
−0.768036 | + | 0.640407i | \(0.778766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 23.7128i | − 0.992350i | −0.868222 | − | 0.496175i | \(-0.834737\pi\) | ||||
0.868222 | − | 0.496175i | \(-0.165263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0718i | 0.587858i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.46410 | −0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.33975 | 0.139035 | 0.0695177 | − | 0.997581i | \(-0.477854\pi\) | ||||
0.0695177 | + | 0.997581i | \(0.477854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 40.3923i | − 1.67865i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.53590i | 0.354129i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46410 | −0.0606369 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.3923i | 0.428936i | 0.976731 | + | 0.214468i | \(0.0688018\pi\) | ||||
−0.976731 | + | 0.214468i | \(0.931198\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.8564 | 0.569976 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.1244 | −1.15493 | −0.577464 | − | 0.816416i | \(-0.695958\pi\) | ||||
−0.577464 | + | 0.816416i | \(0.695958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.26795i | 0.0929769i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 30.2487i | − 1.23800i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.51666 | 0.102828 | 0.0514140 | − | 0.998677i | \(-0.483627\pi\) | ||||
0.0514140 | + | 0.998677i | \(0.483627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.4641 | 1.44661 | 0.723305 | − | 0.690528i | \(-0.242622\pi\) | ||||
0.723305 | + | 0.690528i | \(0.242622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 10.0000i | − 0.406558i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.92820 | −0.321796 | −0.160898 | − | 0.986971i | \(-0.551439\pi\) | ||||
−0.160898 | + | 0.986971i | \(0.551439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.07180 | −0.0839534 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 9.92820i | − 0.401652i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 39.1769i | − 1.58234i | −0.611596 | − | 0.791170i | \(-0.709472\pi\) | ||||
0.611596 | − | 0.791170i | \(-0.290528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.07180 | 0.204515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32051 | −0.0531617 | −0.0265808 | − | 0.999647i | \(-0.508462\pi\) | ||||
−0.0265808 | + | 0.999647i | \(0.508462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 20.5359i | − 0.825407i | −0.910865 | − | 0.412704i | \(-0.864584\pi\) | ||||
0.910865 | − | 0.412704i | \(-0.135416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000i | 0.722315i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.53590 | 0.101599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.46410i | − 0.138343i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.21539i | 0.0484608i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9808 | −1.67123 | −0.835614 | − | 0.549317i | \(-0.814888\pi\) | ||||
−0.835614 | + | 0.549317i | \(0.814888\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.73205 | −0.0688428 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 0.392305i | − 0.0155681i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.00000i | − 0.0396214i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.7128 | −0.857605 | −0.428802 | − | 0.903398i | \(-0.641064\pi\) | ||||
−0.428802 | + | 0.903398i | \(0.641064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 14.8038i | − 0.583807i | −0.956448 | − | 0.291903i | \(-0.905711\pi\) | ||||
0.956448 | − | 0.291903i | \(-0.0942886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000i | 0.236250i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8564 | −1.48829 | −0.744144 | − | 0.668019i | \(-0.767143\pi\) | ||||
−0.744144 | + | 0.668019i | \(0.767143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.46410 | −0.371498 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.92820i | 0.271538i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 16.9282i | − 0.662452i | −0.943551 | − | 0.331226i | \(-0.892538\pi\) | ||||
0.943551 | − | 0.331226i | \(-0.107462\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3923 | −0.406061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.8564i | 1.35781i | 0.734225 | + | 0.678906i | \(0.237546\pi\) | ||||
−0.734225 | + | 0.678906i | \(0.762454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9282i | 0.580640i | 0.956930 | + | 0.290320i | \(0.0937617\pi\) | ||||
−0.956930 | + | 0.290320i | \(0.906238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.92820 | −0.152559 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.14359i | 0.160441i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 32.6603i | − 1.26272i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.46410 | −0.0565210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.60770 | −0.139066 | −0.0695332 | − | 0.997580i | \(-0.522151\pi\) | ||||
−0.0695332 | + | 0.997580i | \(0.522151\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5.19615i | − 0.200000i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7128i | 0.488593i | 0.969701 | + | 0.244297i | \(0.0785570\pi\) | ||||
−0.969701 | + | 0.244297i | \(0.921443\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.7321 | −0.680494 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0718 | −0.539232 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 42.2487i | − 1.61660i | −0.588769 | − | 0.808301i | \(-0.700387\pi\) | ||||
0.588769 | − | 0.808301i | \(-0.299613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.3923i | 0.626318i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564 | 0.528655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.46410 | 0.0557778 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.14359i | 0.0815461i | 0.999168 | + | 0.0407731i | \(0.0129821\pi\) | ||||
−0.999168 | + | 0.0407731i | \(0.987018\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.9282 | 0.793852 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.64102 | −0.251546 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.9282i | 0.715930i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0526i | 0.719605i | 0.933028 | + | 0.359803i | \(0.117156\pi\) | ||||
−0.933028 | + | 0.359803i | \(0.882844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07180 | 0.0404236 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.1962 | 0.647645 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.3923i | 0.541278i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.2679i | 1.43718i | 0.695432 | + | 0.718591i | \(0.255213\pi\) | ||||
−0.695432 | + | 0.718591i | \(0.744787\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8564 | 0.518927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.00000i | − 0.0373979i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.00000i | − 0.112037i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0000 | −0.522112 | −0.261056 | − | 0.965324i | \(-0.584071\pi\) | ||||
−0.261056 | + | 0.965324i | \(0.584071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.92820 | 0.295262 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.1436i | 0.600387i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.19615i | − 0.0444240i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.5692 | −1.83842 | −0.919210 | − | 0.393767i | \(-0.871172\pi\) | ||||
−0.919210 | + | 0.393767i | \(0.871172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 7.85641i | − 0.290580i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.21539i | 0.155699i | 0.996965 | + | 0.0778495i | \(0.0248054\pi\) | ||||
−0.996965 | + | 0.0778495i | \(0.975195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.73205 | 0.0638877 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.46410 | 0.201273 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 39.7846i | − 1.46350i | −0.681573 | − | 0.731750i | \(-0.738704\pi\) | ||||
0.681573 | − | 0.731750i | \(-0.261296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.46410i | 0.127257i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.2487 | 0.669480 | 0.334740 | − | 0.942310i | \(-0.391351\pi\) | ||||
0.334740 | + | 0.942310i | \(0.391351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8564 | 0.800757 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 3.07180i | − 0.112241i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.1244 | −1.17223 | −0.586117 | − | 0.810226i | \(-0.699344\pi\) | ||||
−0.586117 | + | 0.810226i | \(0.699344\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1769 | −0.698846 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.660254i | 0.0240291i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 7.71281i | − 0.280327i | −0.990128 | − | 0.140163i | \(-0.955237\pi\) | ||||
0.990128 | − | 0.140163i | \(-0.0447628\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3923 | −0.956720 | −0.478360 | − | 0.878164i | \(-0.658769\pi\) | ||||
−0.478360 | + | 0.878164i | \(0.658769\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.80385i | − 0.101506i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.46410 | 0.341729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.2487 | −0.441700 | −0.220850 | − | 0.975308i | \(-0.570883\pi\) | ||||
−0.220850 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 36.0000i | − 1.29651i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.8564i | 0.822088i | 0.911616 | + | 0.411044i | \(0.134836\pi\) | ||||
−0.911616 | + | 0.411044i | \(0.865164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.928203 | 0.0332991 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.85641i | 0.209828i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.46410i | 0.267087i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.21539 | −0.222120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.92820 | −0.175895 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5167i | 1.37297i | 0.727144 | + | 0.686485i | \(0.240847\pi\) | ||||
−0.727144 | + | 0.686485i | \(0.759153\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.7846i | 0.953557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.92820 | 0.175227 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.46410 | 0.0519918 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.53590i | 0.0899390i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.5692i | 1.57872i | 0.613929 | + | 0.789361i | \(0.289588\pi\) | ||||
−0.613929 | + | 0.789361i | \(0.710412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.5167 | −0.796582 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00000i | 0.141157i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.46410i | − 0.122094i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.7846 | 0.942863 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.7128 | −0.657907 | −0.328954 | − | 0.944346i | \(-0.606696\pi\) | ||||
−0.328954 | + | 0.944346i | \(0.606696\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 32.9282i | − 1.15627i | −0.815943 | − | 0.578133i | \(-0.803782\pi\) | ||||
0.815943 | − | 0.578133i | \(-0.196218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.1769i | 0.882993i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.4641 | −0.401570 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.92820 | −0.242387 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.4449i | 0.469229i | 0.972088 | + | 0.234614i | \(0.0753828\pi\) | ||||
−0.972088 | + | 0.234614i | \(0.924617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.6410 | 1.06808 | 0.534039 | − | 0.845460i | \(-0.320673\pi\) | ||||
0.534039 | + | 0.845460i | \(0.320673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.73205 | 0.0603023 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.4641i | 1.37230i | 0.727459 | + | 0.686151i | \(0.240701\pi\) | ||||
−0.727459 | + | 0.686151i | \(0.759299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 43.7128i | − 1.51821i | −0.650969 | − | 0.759104i | \(-0.725637\pi\) | ||||
0.650969 | − | 0.759104i | \(-0.274363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.2487 | 1.67373 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.26795 | −0.0785798 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.92820i | 0.274367i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.7846i | 0.718421i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.5692 | 1.64227 | 0.821136 | − | 0.570733i | \(-0.193341\pi\) | ||||
0.821136 | + | 0.570733i | \(0.193341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.5692 | 0.950663 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.1244i | 1.65749i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 12.0000i | − 0.412813i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.9282 | −0.958493 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.85641i | − 0.0636368i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 34.0000i | − 1.16414i | −0.813139 | − | 0.582069i | \(-0.802243\pi\) | ||||
0.813139 | − | 0.582069i | \(-0.197757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.00000 | −0.136637 | −0.0683187 | − | 0.997664i | \(-0.521763\pi\) | ||||
−0.0683187 | + | 0.997664i | \(0.521763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 22.6410i | − 0.772502i | −0.922394 | − | 0.386251i | \(-0.873770\pi\) | ||||
0.922394 | − | 0.386251i | \(-0.126230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.07180i | 0.172846i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.9282 | −1.59745 | −0.798727 | − | 0.601693i | \(-0.794493\pi\) | ||||
−0.798727 | + | 0.601693i | \(0.794493\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.00000 | 0.170005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 20.5359i | − 0.697436i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.26795i | 0.0769349i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.46410 | −0.185144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 37.7128i | − 1.27347i | −0.771082 | − | 0.636736i | \(-0.780284\pi\) | ||||
0.771082 | − | 0.636736i | \(-0.219716\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.1244 | 1.21844 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.5692 | 1.67003 | 0.835015 | − | 0.550228i | \(-0.185459\pi\) | ||||
0.835015 | + | 0.550228i | \(0.185459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3205i | 0.515576i | 0.966201 | + | 0.257788i | \(0.0829936\pi\) | ||||
−0.966201 | + | 0.257788i | \(0.917006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3923i | 0.551021i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.7846 | −0.563572 | −0.281786 | − | 0.959477i | \(-0.590927\pi\) | ||||
−0.281786 | + | 0.959477i | \(0.590927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.392305 | 0.0131575 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 9.00000i | − 0.301511i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.8564i | 0.664469i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.07180 | 0.0358262 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000 | 0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.78461i | 0.159576i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.32051i | − 0.110622i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | −0.199667 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.39230 | −0.146005 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 22.7846i | − 0.756551i | −0.925693 | − | 0.378275i | \(-0.876517\pi\) | ||||
0.925693 | − | 0.378275i | \(-0.123483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.60770 | −0.0532653 | −0.0266327 | − | 0.999645i | \(-0.508478\pi\) | ||||
−0.0266327 | + | 0.999645i | \(0.508478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.53590 | −0.282497 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.53590i | 0.0838342i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.3923i | − 0.343184i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.7321 | 1.64051 | 0.820254 | − | 0.571999i | \(-0.193832\pi\) | ||||
0.820254 | + | 0.571999i | \(0.193832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0718 | −0.661388 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 7.46410i | − 0.245684i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.535898i | 0.0176202i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.4641 | −1.09792 | −0.548961 | − | 0.835848i | \(-0.684976\pi\) | ||||
−0.548961 | + | 0.835848i | \(0.684976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000i | 0.0655474i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 11.0718i | − 0.362474i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.26795 | −0.0741699 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.1962 | 0.561774 | 0.280887 | − | 0.959741i | \(-0.409371\pi\) | ||||
0.280887 | + | 0.959741i | \(0.409371\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 6.21539i | − 0.202832i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.67949i | 0.152547i | 0.997087 | + | 0.0762735i | \(0.0243022\pi\) | ||||
−0.997087 | + | 0.0762735i | \(0.975698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1436 | 0.330321 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.19615 | 0.169031 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.0000i | 1.42981i | 0.699223 | + | 0.714904i | \(0.253530\pi\) | ||||
−0.699223 | + | 0.714904i | \(0.746470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.00000i | − 0.129845i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.8564 | 0.643888 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 8.12436i | − 0.262898i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.07180i | − 0.0669717i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.3923 | −0.529335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.3205i | 0.750714i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.5359 | −0.531759 | −0.265879 | − | 0.964006i | \(-0.585662\pi\) | ||||
−0.265879 | + | 0.964006i | \(0.585662\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.85641 | 0.252384 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9282i | 0.670927i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.73205 | −0.0554700 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.60770 | 0.0514347 | 0.0257174 | − | 0.999669i | \(-0.491813\pi\) | ||||
0.0257174 | + | 0.999669i | \(0.491813\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.53590i | 0.0810477i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.7128 | 1.29854 | 0.649269 | − | 0.760559i | \(-0.275075\pi\) | ||||
0.649269 | + | 0.760559i | \(0.275075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00000 | −0.254901 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.1962i | 0.547360i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000i | 0.381578i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.2487 | 1.53267 | 0.766335 | − | 0.642441i | \(-0.222078\pi\) | ||||
0.766335 | + | 0.642441i | \(0.222078\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.8564 | 1.58215 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4641i | 0.553649i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.5692i | 1.34818i | 0.738649 | + | 0.674090i | \(0.235464\pi\) | ||||
−0.738649 | + | 0.674090i | \(0.764536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.78461 | 0.0881012 |
(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 | 2240.2.b.d.1121.3 | yes | 4 | |
4.3 | odd | 2 | 2240.2.b.c.1121.1 | ✓ | 4 | ||
8.3 | odd | 2 | 2240.2.b.c.1121.4 | yes | 4 | ||
8.5 | even | 2 | inner | 2240.2.b.d.1121.2 | yes | 4 | |
16.3 | odd | 4 | 8960.2.a.z.1.2 | 2 | |||
16.5 | even | 4 | 8960.2.a.ba.1.2 | 2 | |||
16.11 | odd | 4 | 8960.2.a.bb.1.1 | 2 | |||
16.13 | even | 4 | 8960.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.c.1121.1 | ✓ | 4 | 4.3 | odd | 2 | ||
2240.2.b.c.1121.4 | yes | 4 | 8.3 | odd | 2 | ||
2240.2.b.d.1121.2 | yes | 4 | 8.5 | even | 2 | inner | |
2240.2.b.d.1121.3 | yes | 4 | 1.1 | even | 1 | trivial | |
8960.2.a.y.1.1 | 2 | 16.13 | even | 4 | |||
8960.2.a.z.1.2 | 2 | 16.3 | odd | 4 | |||
8960.2.a.ba.1.2 | 2 | 16.5 | even | 4 | |||
8960.2.a.bb.1.1 | 2 | 16.11 | odd | 4 |