Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,2,Mod(129,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.c (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: | \(5.11042572936\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.5 | ||
Root | \(-0.854638 + 0.854638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.129 |
Dual form | 640.2.c.b.129.2 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.70928i | 0.986851i | 0.869788 | + | 0.493425i | \(0.164255\pi\) | ||||
−0.869788 | + | 0.493425i | \(0.835745\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17009 | − | 0.539189i | −0.970492 | − | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.63090i | − | 0.994386i | −0.867640 | − | 0.497193i | \(-0.834364\pi\) | ||
0.867640 | − | 0.497193i | \(-0.165636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0783777 | 0.0261259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.41855 | 1.63375 | 0.816877 | − | 0.576812i | \(-0.195703\pi\) | ||||
0.816877 | + | 0.576812i | \(0.195703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.34017i | 1.75845i | 0.476409 | + | 0.879224i | \(0.341938\pi\) | ||||
−0.476409 | + | 0.879224i | \(0.658062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.921622 | − | 3.70928i | 0.237962 | − | 0.957731i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.41855i | 0.829120i | 0.910022 | + | 0.414560i | \(0.136065\pi\) | ||||
−0.910022 | + | 0.414560i | \(0.863935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26180 | −0.748307 | −0.374154 | − | 0.927367i | \(-0.622067\pi\) | ||||
−0.374154 | + | 0.927367i | \(0.622067\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.49693 | 0.981310 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.36910i | 0.285478i | 0.989760 | + | 0.142739i | \(0.0455909\pi\) | ||||
−0.989760 | + | 0.142739i | \(0.954409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | + | 2.34017i | 0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.26180i | 1.01263i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.68035 | 0.840615 | 0.420307 | − | 0.907382i | \(-0.361922\pi\) | ||||
0.420307 | + | 0.907382i | \(0.361922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.26180i | 1.61227i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41855 | + | 5.70928i | −0.239779 | + | 0.965044i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.75872i | 0.946728i | 0.880867 | + | 0.473364i | \(0.156961\pi\) | ||||
−0.880867 | + | 0.473364i | \(0.843039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8371 | −1.73533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.75872 | −1.21171 | −0.605855 | − | 0.795575i | \(-0.707169\pi\) | ||||
−0.605855 | + | 0.795575i | \(0.707169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.44748i | − | 0.678234i | −0.940744 | − | 0.339117i | \(-0.889872\pi\) | ||
0.940744 | − | 0.339117i | \(-0.110128\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.170086 | − | 0.0422604i | −0.0253550 | − | 0.00629981i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.78765i | − | 0.698351i | −0.937057 | − | 0.349175i | \(-0.886462\pi\) | ||
0.937057 | − | 0.349175i | \(-0.113538\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0783777 | 0.0111968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.84324 | −0.818218 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.65983i | 0.227995i | 0.993481 | + | 0.113997i | \(0.0363656\pi\) | ||||
−0.993481 | + | 0.113997i | \(0.963634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.7587 | − | 2.92162i | −1.58555 | − | 0.393951i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.57531i | − | 0.738467i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.26180 | 0.424650 | 0.212325 | − | 0.977199i | \(-0.431897\pi\) | ||||
0.212325 | + | 0.977199i | \(0.431897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.49693 | 0.319699 | 0.159849 | − | 0.987141i | \(-0.448899\pi\) | ||||
0.159849 | + | 0.987141i | \(0.448899\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.206204i | − | 0.0259792i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.41855 | − | 13.7587i | 0.424019 | − | 1.70656i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.86603i | 0.960989i | 0.876998 | + | 0.480494i | \(0.159543\pi\) | ||||
−0.876998 | + | 0.480494i | \(0.840457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.34017 | −0.281724 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.15676 | 0.730672 | 0.365336 | − | 0.930876i | \(-0.380954\pi\) | ||||
0.365336 | + | 0.930876i | \(0.380954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5753i | 1.58887i | 0.607350 | + | 0.794435i | \(0.292233\pi\) | ||||
−0.607350 | + | 0.794435i | \(0.707767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.00000 | + | 7.55252i | −0.461880 | + | 0.872090i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 14.2557i | − | 1.62458i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.6803 | 1.42665 | 0.713325 | − | 0.700833i | \(-0.247188\pi\) | ||||
0.713325 | + | 0.700833i | \(0.247188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.75872 | −0.973192 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.9711i | − | 1.64329i | −0.570001 | − | 0.821644i | \(-0.693057\pi\) | ||
0.570001 | − | 0.821644i | \(-0.306943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.84324 | − | 7.41855i | 0.199928 | − | 0.804655i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41855i | 0.366507i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.52359 | 0.903499 | 0.451749 | − | 0.892145i | \(-0.350800\pi\) | ||||
0.451749 | + | 0.892145i | \(0.350800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.6803 | 1.74858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000i | 0.829561i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.07838 | + | 1.75872i | 0.726226 | + | 0.180441i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.58145i | − | 0.465176i | −0.972575 | − | 0.232588i | \(-0.925281\pi\) | ||
0.972575 | − | 0.232588i | \(-0.0747193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.424694 | 0.0426833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.31351 | −0.230203 | −0.115101 | − | 0.993354i | \(-0.536719\pi\) | ||||
−0.115101 | + | 0.993354i | \(0.536719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2062i | 1.59684i | 0.602098 | + | 0.798422i | \(0.294332\pi\) | ||||
−0.602098 | + | 0.798422i | \(0.705668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.75872 | − | 2.42469i | −0.952354 | − | 0.236626i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.6514i | − | 1.51308i | −0.653948 | − | 0.756540i | \(-0.726888\pi\) | ||
0.653948 | − | 0.756540i | \(-0.273112\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.3402 | −1.18197 | −0.590987 | − | 0.806681i | \(-0.701262\pi\) | ||||
−0.590987 | + | 0.806681i | \(0.701262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.84324 | −0.934279 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.36069i | − | 0.880580i | −0.897856 | − | 0.440290i | \(-0.854876\pi\) | ||
0.897856 | − | 0.440290i | \(-0.145124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.738205 | − | 2.97107i | 0.0688379 | − | 0.277054i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.496928i | 0.0459411i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.99386 | 0.824466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3607 | 1.66915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 13.2618i | − | 1.19578i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.32684 | − | 7.46081i | −0.744775 | − | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.95055i | − | 0.173083i | −0.996248 | − | 0.0865417i | \(-0.972418\pi\) | ||
0.996248 | − | 0.0865417i | \(-0.0275816\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.60197 | 0.669316 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5753 | −1.36082 | −0.680410 | − | 0.732831i | \(-0.738198\pi\) | ||||
−0.680410 | + | 0.732831i | \(0.738198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.58145i | 0.744106i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.83710 | − | 11.4186i | 0.244179 | − | 0.982752i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.2039i | − | 1.29896i | −0.760379 | − | 0.649480i | \(-0.774987\pi\) | ||
0.760379 | − | 0.649480i | \(-0.225013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.58145 | −0.218956 | −0.109478 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109478 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.18342 | 0.689168 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34.3545i | 2.87287i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34017 | − | 1.07838i | −0.360432 | − | 0.0895544i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.133969i | 0.0110496i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.81658 | −0.148820 | −0.0744101 | − | 0.997228i | \(-0.523707\pi\) | ||||
−0.0744101 | + | 0.997228i | \(0.523707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.16290 | 0.420151 | 0.210075 | − | 0.977685i | \(-0.432629\pi\) | ||||
0.210075 | + | 0.977685i | \(0.432629\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.267938i | 0.0216615i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.1568 | − | 2.52359i | −0.815810 | − | 0.202700i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.7587i | − | 1.09807i | −0.835801 | − | 0.549033i | \(-0.814996\pi\) | ||
0.835801 | − | 0.549033i | \(-0.185004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.83710 | −0.224997 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.60197 | 0.283875 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.29072i | − | 0.492728i | −0.969177 | − | 0.246364i | \(-0.920764\pi\) | ||
0.969177 | − | 0.246364i | \(-0.0792358\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.99386 | − | 20.0989i | 0.388771 | − | 1.56470i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.89269i | 0.301226i | 0.988593 | + | 0.150613i | \(0.0481247\pi\) | ||||
−0.988593 | + | 0.150613i | \(0.951875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.1978 | −2.09214 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.255652 | −0.0195502 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.44521i | − | 0.109877i | −0.998490 | − | 0.0549387i | \(-0.982504\pi\) | ||
0.998490 | − | 0.0549387i | \(-0.0174964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.15676 | − | 11.6248i | 0.465407 | − | 0.878749i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.57531i | 0.419066i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9421 | 0.892598 | 0.446299 | − | 0.894884i | \(-0.352742\pi\) | ||||
0.446299 | + | 0.894884i | \(0.352742\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3607 | −1.14175 | −0.570876 | − | 0.821037i | \(-0.693396\pi\) | ||||
−0.570876 | + | 0.821037i | \(0.693396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.26794i | 0.315495i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.10504 | − | 12.4969i | 0.228287 | − | 0.918792i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5236i | 1.35458i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8432 | 1.00695 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.3607 | −1.83504 | −0.917518 | − | 0.397695i | \(-0.869810\pi\) | ||||
−0.917518 | + | 0.397695i | \(0.869810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.58145i | 0.329780i | 0.986312 | + | 0.164890i | \(0.0527269\pi\) | ||||
−0.986312 | + | 0.164890i | \(0.947273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.5174 | + | 5.84324i | 1.68412 | + | 0.418443i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.8638i | − | 1.20149i | −0.799439 | − | 0.600747i | \(-0.794870\pi\) | ||
0.799439 | − | 0.600747i | \(-0.205130\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.84324 | −0.697769 | −0.348885 | − | 0.937166i | \(-0.613439\pi\) | ||||
−0.348885 | + | 0.937166i | \(0.613439\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4452 | −0.948352 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.26180i | − | 0.369306i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8371 | + | 4.18342i | 1.17595 | + | 0.292183i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.107307i | 0.00745836i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.6742 | −1.22255 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5753 | −1.07225 | −0.536124 | − | 0.844139i | \(-0.680112\pi\) | ||||
−0.536124 | + | 0.844139i | \(0.680112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5236i | 0.721065i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.39803 | + | 9.65142i | −0.163544 | + | 0.658221i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.3135i | − | 0.835896i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.2039 | −1.56798 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.6742 | −1.45796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.9854i | − | 1.13743i | −0.822535 | − | 0.568715i | \(-0.807441\pi\) | ||
0.822535 | − | 0.568715i | \(-0.192559\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.346316 | + | 0.183417i | 0.0230877 | + | 0.0122278i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.9649i | − | 1.32512i | −0.749009 | − | 0.662559i | \(-0.769470\pi\) | ||
0.749009 | − | 0.662559i | \(-0.230530\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.6742 | 1.56444 | 0.782218 | − | 0.623005i | \(-0.214088\pi\) | ||||
0.782218 | + | 0.623005i | \(0.214088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.3668 | 1.60322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5753i | 0.889348i | 0.895693 | + | 0.444674i | \(0.146680\pi\) | ||||
−0.895693 | + | 0.444674i | \(0.853320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58145 | + | 10.3896i | −0.168395 | + | 0.677744i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.6742i | 1.40789i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.36683 | −0.541206 | −0.270603 | − | 0.962691i | \(-0.587223\pi\) | ||||
−0.270603 | + | 0.962691i | \(0.587223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.91548 | 0.638712 | 0.319356 | − | 0.947635i | \(-0.396533\pi\) | ||||
0.319356 | + | 0.947635i | \(0.396533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.814315i | 0.0522383i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.170086 | − | 0.0422604i | −0.0108664 | − | 0.00269992i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 20.6803i | − | 1.31586i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.5897 | 1.62168 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.6163 | −1.11193 | −0.555967 | − | 0.831204i | \(-0.687652\pi\) | ||||
−0.555967 | + | 0.831204i | \(0.687652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.41855i | 0.466400i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.6803 | + | 3.15061i | 0.794074 | + | 0.197299i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.68649i | 0.229957i | 0.993368 | + | 0.114978i | \(0.0366799\pi\) | ||||
−0.993368 | + | 0.114978i | \(0.963320\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.1506 | 0.941413 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156755 | 0.00970292 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.107307i | − | 0.00661684i | −0.999995 | − | 0.00330842i | \(-0.998947\pi\) | ||
0.999995 | − | 0.00330842i | \(-0.00105311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.894960 | − | 3.60197i | 0.0549770 | − | 0.221267i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5692i | 0.891618i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.85762 | 0.235203 | 0.117602 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117602 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3074 | −1.29433 | −0.647165 | − | 0.762350i | \(-0.724046\pi\) | ||||
−0.647165 | + | 0.762350i | \(0.724046\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.5113i | 1.72558i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.9421 | + | 12.6803i | 1.44377 | + | 0.764654i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.44521i | 0.0868344i | 0.999057 | + | 0.0434172i | \(0.0138245\pi\) | ||||
−0.999057 | + | 0.0434172i | \(0.986176\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.366835 | 0.0219618 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4391 | 0.742053 | 0.371026 | − | 0.928622i | \(-0.379006\pi\) | ||||
0.371026 | + | 0.928622i | \(0.379006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 6.29072i | − | 0.373945i | −0.982365 | − | 0.186972i | \(-0.940133\pi\) | ||
0.982365 | − | 0.186972i | \(-0.0598675\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00614 | + | 12.0989i | −0.178069 | + | 0.716677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.4124i | 1.20491i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.31351 | 0.312559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.83096 | 0.459059 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.07838i | − | 0.0629995i | −0.999504 | − | 0.0314998i | \(-0.989972\pi\) | ||
0.999504 | − | 0.0314998i | \(-0.0100283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.07838 | − | 1.75872i | −0.412119 | − | 0.102397i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 28.5113i | 1.65439i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.68035 | −0.501997 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7009 | −0.674427 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.95443i | − | 0.227176i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.41855 | − | 1.34632i | −0.310265 | − | 0.0770898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2267i | 1.43977i | 0.694096 | + | 0.719883i | \(0.255804\pi\) | ||||
−0.694096 | + | 0.719883i | \(0.744196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.7009 | −1.57585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.8371 | 1.06815 | 0.534077 | − | 0.845436i | \(-0.320659\pi\) | ||||
0.534077 | + | 0.845436i | \(0.320659\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2039i | 0.859377i | 0.902977 | + | 0.429689i | \(0.141377\pi\) | ||||
−0.902977 | + | 0.429689i | \(0.858623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.111183 | + | 0.447480i | −0.00626444 | + | 0.0252126i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.8638i | 0.947163i | 0.880750 | + | 0.473582i | \(0.157039\pi\) | ||||
−0.880750 | + | 0.473582i | \(0.842961\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8371 | 0.606761 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.7526 | 1.49318 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.1506i | − | 0.620437i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.8371 | + | 28.0144i | −0.823014 | + | 1.55396i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 21.0928i | − | 1.16643i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.5958 | −0.694430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5753 | 1.29582 | 0.647908 | − | 0.761719i | \(-0.275644\pi\) | ||||
0.647908 | + | 0.761719i | \(0.275644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.451356i | 0.0247341i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.24128 | − | 17.0700i | 0.231726 | − | 0.932632i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14.8371i | − | 0.808228i | −0.914709 | − | 0.404114i | \(-0.867580\pi\) | ||
0.914709 | − | 0.404114i | \(-0.132420\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3607 | 1.37336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.6225i | − | 1.00552i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.07838 | + | 1.26180i | 0.273411 | + | 0.0679328i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.133969i | − | 0.00719184i | −0.999994 | − | 0.00359592i | \(-0.998855\pi\) | ||
0.999994 | − | 0.00359592i | \(-0.00114462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.3135 | 1.19441 | 0.597207 | − | 0.802087i | \(-0.296277\pi\) | ||||
0.597207 | + | 0.802087i | \(0.296277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.3607 | −1.78066 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.8371i | − | 1.21550i | −0.794130 | − | 0.607748i | \(-0.792073\pi\) | ||
0.794130 | − | 0.607748i | \(-0.207927\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.3607 | − | 3.31965i | −0.709112 | − | 0.176189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.3730i | 0.813624i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.8843 | 1.68279 | 0.841394 | − | 0.540422i | \(-0.181735\pi\) | ||||
0.841394 | + | 0.540422i | \(0.181735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.36069 | −0.440036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.3835i | 1.64721i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.31965 | − | 29.4596i | 0.383128 | − | 1.54199i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 30.4619i | − | 1.59010i | −0.606547 | − | 0.795048i | \(-0.707446\pi\) | ||
0.606547 | − | 0.795048i | \(-0.292554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.608111 | −0.0316570 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.36683 | 0.226715 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0722i | 0.521521i | 0.965404 | + | 0.260760i | \(0.0839732\pi\) | ||||
−0.965404 | + | 0.260760i | \(0.916027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.7526 | − | 14.2329i | 0.658540 | − | 0.734982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.6803i | 0.653071i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7792 | 0.759159 | 0.379579 | − | 0.925159i | \(-0.376069\pi\) | ||||
0.379579 | + | 0.925159i | \(0.376069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.33403 | 0.170808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 14.4619i | − | 0.738966i | −0.929237 | − | 0.369483i | \(-0.879535\pi\) | ||
0.929237 | − | 0.369483i | \(-0.120465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.68649 | + | 30.9360i | −0.391740 | + | 1.57664i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.348583i | − | 0.0177195i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.17727 | −0.161094 | −0.0805471 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805471 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.68035 | −0.236695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 26.6225i | − | 1.34293i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.5174 | − | 6.83710i | −1.38455 | − | 0.344012i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.8227i | − | 0.543177i | −0.962413 | − | 0.271589i | \(-0.912451\pi\) | ||
0.962413 | − | 0.271589i | \(-0.0875490\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6681 | −0.734321 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5236 | −0.625398 | −0.312699 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312699 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.6742i | 1.47818i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.0072 | + | 4.72261i | 0.944475 | + | 0.234668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.2039i | 1.54672i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2885 | 0.657072 | 0.328536 | − | 0.944491i | \(-0.393445\pi\) | ||||
0.328536 | + | 0.944491i | \(0.393445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.9877 | 1.28188 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.58145i | − | 0.422266i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.07223 | + | 32.4885i | −0.396250 | + | 1.59480i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.41241i | − | 0.216077i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.255652 | 0.0124894 | 0.00624471 | − | 0.999981i | \(-0.498012\pi\) | ||||
0.00624471 | + | 0.999981i | \(0.498012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.49693 | 0.121693 | 0.0608464 | − | 0.998147i | \(-0.480620\pi\) | ||||
0.0608464 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.375245i | − | 0.0182451i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.00000 | + | 15.1050i | −0.388057 | + | 0.732702i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.56916i | − | 0.317904i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −58.7214 | −2.83510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.993857 | 0.0478724 | 0.0239362 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239362 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6286i | 0.847178i | 0.905855 | + | 0.423589i | \(0.139230\pi\) | ||||
−0.905855 | + | 0.423589i | \(0.860770\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.84324 | − | 7.41855i | 0.0883768 | − | 0.355692i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.46573i | − | 0.213625i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.5113 | −1.93350 | −0.966750 | − | 0.255725i | \(-0.917686\pi\) | ||||
−0.966750 | + | 0.255725i | \(0.917686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.00614307 | 0.000292527 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7093i | 0.841393i | 0.907201 | + | 0.420697i | \(0.138214\pi\) | ||||
−0.907201 | + | 0.420697i | \(0.861786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.4969 | − | 4.59583i | −0.876839 | − | 0.217863i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 3.10504i | − | 0.146863i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.28846 | 0.0608061 | 0.0304030 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304030 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.0410 | −1.97964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82482i | 0.414626i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −36.1978 | − | 8.99386i | −1.69698 | − | 0.421639i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3545i | 1.23281i | 0.787428 | + | 0.616407i | \(0.211412\pi\) | ||||
−0.787428 | + | 0.616407i | \(0.788588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.9877 | −0.839595 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.0349 | 1.91119 | 0.955593 | − | 0.294690i | \(-0.0952165\pi\) | ||||
0.955593 | + | 0.294690i | \(0.0952165\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7708i | 1.33709i | 0.743670 | + | 0.668547i | \(0.233083\pi\) | ||||
−0.743670 | + | 0.668547i | \(0.766917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.31351 | − | 17.3607i | 0.200034 | − | 0.805083i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 5.12783i | − | 0.237287i | −0.992937 | − | 0.118644i | \(-0.962145\pi\) | ||
0.992937 | − | 0.118644i | \(-0.0378546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.6947 | 0.955593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.5174 | 1.08363 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 24.0989i | − | 1.10807i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.4124 | − | 7.63317i | −0.661287 | − | 0.350234i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.130094i | 0.00595657i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6742 | 0.624790 | 0.312395 | − | 0.949952i | \(-0.398869\pi\) | ||||
0.312395 | + | 0.949952i | \(0.398869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.5113 | −1.66477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.15676i | 0.280142i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.47027 | + | 9.94214i | −0.112169 | + | 0.451449i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.51971i | 0.386065i | 0.981192 | + | 0.193033i | \(0.0618323\pi\) | ||||
−0.981192 | + | 0.193033i | \(0.938168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.7526 | 0.486249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.73820 | −0.213832 | −0.106916 | − | 0.994268i | \(-0.534098\pi\) | ||||
−0.106916 | + | 0.994268i | \(0.534098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83710i | 0.307928i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.921622 | − | 0.228990i | −0.0414238 | − | 0.0102923i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 16.1978i | − | 0.726570i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0928 | −0.496580 | −0.248290 | − | 0.968686i | \(-0.579869\pi\) | ||||
−0.248290 | + | 0.968686i | \(0.579869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.65368 | −0.297265 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.42082i | − | 0.375466i | −0.982220 | − | 0.187733i | \(-0.939886\pi\) | ||
0.982220 | − | 0.187733i | \(-0.0601139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.02052 | + | 1.24742i | 0.223410 | + | 0.0555094i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 46.4885i | − | 2.06463i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.0000 | 1.15243 | 0.576215 | − | 0.817298i | \(-0.304529\pi\) | ||||
0.576215 | + | 0.817298i | \(0.304529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.7152 | 1.57995 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 17.1629i | − | 0.757760i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.73820 | − | 35.1689i | 0.385051 | − | 1.54973i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 25.9421i | − | 1.14093i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.47027 | 0.108433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3135 | −0.451843 | −0.225922 | − | 0.974145i | \(-0.572539\pi\) | ||||
−0.225922 | + | 0.974145i | \(0.572539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.2784i | − | 0.711806i | −0.934523 | − | 0.355903i | \(-0.884173\pi\) | ||
0.934523 | − | 0.355903i | \(-0.115827\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.8699 | + | 10.5236i | 0.867194 | + | 0.459287i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0000i | 0.696971i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1256 | 0.918503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.255652 | 0.0110944 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 49.1917i | − | 2.13073i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.43907 | + | 33.9649i | −0.364853 | + | 1.46843i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.4124i | 0.880860i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.424694 | 0.0182929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.36069 | 0.144487 | 0.0722437 | − | 0.997387i | \(-0.476984\pi\) | ||||
0.0722437 | + | 0.997387i | \(0.476984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 26.2557i | − | 1.12674i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.7792 | + | 6.65368i | 1.14710 | + | 0.285013i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.51148i | 0.0646263i | 0.999478 | + | 0.0323132i | \(0.0102874\pi\) | ||||
−0.999478 | + | 0.0323132i | \(0.989713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.195704 | 0.00835243 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.52359 | −0.277914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 33.3607i | − | 1.41864i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.3607 | + | 5.30737i | 0.906711 | + | 0.225285i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.2290i | 1.53507i | 0.641006 | + | 0.767536i | \(0.278517\pi\) | ||||
−0.641006 | + | 0.767536i | \(0.721483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.1978 | 1.19264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.6619 | −1.33677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.17501i | − | 0.0916656i | −0.998949 | − | 0.0458328i | \(-0.985406\pi\) | ||
0.998949 | − | 0.0458328i | \(-0.0145941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.04718 | + | 20.3135i | −0.212336 | + | 0.854596i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.0433i | 0.967728i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.1194 | −1.38844 | −0.694219 | − | 0.719764i | \(-0.744250\pi\) | ||||
−0.694219 | + | 0.719764i | \(0.744250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.4657 | 0.772767 | 0.386383 | − | 0.922338i | \(-0.373724\pi\) | ||||
0.386383 | + | 0.922338i | \(0.373724\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 43.3484i | − | 1.81091i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.20394 | + | 6.04945i | −0.133613 | + | 0.252279i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 14.2101i | − | 0.591573i | −0.955254 | − | 0.295787i | \(-0.904418\pi\) | ||
0.955254 | − | 0.295787i | \(-0.0955818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.83096 | −0.325444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.3874 | −1.63406 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.99386i | 0.372487i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.267938 | − | 1.07838i | 0.0110779 | − | 0.0445854i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7503i | 0.484987i | 0.970153 | + | 0.242494i | \(0.0779654\pi\) | ||||
−0.970153 | + | 0.242494i | \(0.922035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.2663 | −0.629038 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.8248 | 1.18569 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.00000i | − | 0.328521i | −0.986417 | − | 0.164260i | \(-0.947476\pi\) | ||
0.986417 | − | 0.164260i | \(-0.0525237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5174 | − | 4.84939i | −0.800137 | − | 0.198806i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.8248i | − | 0.688594i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.5646 | −0.840248 | −0.420124 | − | 0.907467i | \(-0.638013\pi\) | ||||
−0.420124 | + | 0.907467i | \(0.638013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.60811 | −0.351132 | −0.175566 | − | 0.984468i | \(-0.556176\pi\) | ||||
−0.175566 | + | 0.984468i | \(0.556176\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.616522i | 0.0251067i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −39.8443 | − | 9.89988i | −1.61990 | − | 0.402487i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.259528i | 0.0105339i | 0.999986 | + | 0.00526695i | \(0.00167653\pi\) | ||||
−0.999986 | + | 0.00526695i | \(0.998323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.99386 | 0.364449 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.3545 | 1.22801 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.1650i | − | 1.90498i | −0.304576 | − | 0.952488i | \(-0.598515\pi\) | ||
0.304576 | − | 0.952488i | \(-0.401485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.15061 | + | 28.7792i | −0.288341 | + | 1.16049i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 40.2967i | − | 1.62228i | −0.584849 | − | 0.811142i | \(-0.698846\pi\) | ||
0.584849 | − | 0.811142i | \(-0.301154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.6102 | 1.23033 | 0.615164 | − | 0.788399i | \(-0.289090\pi\) | ||||
0.615164 | + | 0.788399i | \(0.289090\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.20394 | −0.289084 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 22.4247i | − | 0.898426i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | + | 20.6803i | 0.561887 | + | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 30.2101i | − | 1.20647i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.6865 | −0.784952 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.21008 | −0.0879819 | −0.0439909 | − | 0.999032i | \(-0.514007\pi\) | ||||
−0.0439909 | + | 0.999032i | \(0.514007\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 26.6225i | − | 1.05815i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.05172 | + | 4.23287i | −0.0417361 | + | 0.167976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.496928i | 0.0196890i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.482553 | 0.0190895 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.92777 | 0.313128 | 0.156564 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156564 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.18115i | − | 0.204325i | −0.994768 | − | 0.102162i | \(-0.967424\pi\) | ||
0.994768 | − | 0.102162i | \(-0.0325761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4969 | − | 4.09890i | −0.649566 | − | 0.161394i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2062i | 0.479875i | 0.970788 | + | 0.239938i | \(0.0771270\pi\) | ||||
−0.970788 | + | 0.239938i | \(0.922873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.6742 | 0.693773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.0472 | 0.824904 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 32.4969i | − | 1.27170i | −0.771811 | − | 0.635852i | \(-0.780649\pi\) | ||
0.771811 | − | 0.635852i | \(-0.219351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.7998 | + | 8.39803i | 1.32067 | + | 0.328138i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.06400i | 0.0415107i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4186 | −1.14598 | −0.572992 | − | 0.819561i | \(-0.694217\pi\) | ||||
−0.572992 | + | 0.819561i | \(0.694217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.0677 | 1.01392 | 0.506958 | − | 0.861971i | \(-0.330770\pi\) | ||||
0.506958 | + | 0.861971i | \(0.330770\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 37.0472i | − | 1.43879i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.62702 | − | 18.6225i | 0.179428 | − | 0.722149i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.73820i | 0.106024i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.0328 | 1.12247 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5297 | 0.522310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.62863i | − | 0.371156i | −0.982629 | − | 0.185578i | \(-0.940584\pi\) | ||
0.982629 | − | 0.185578i | \(-0.0594158\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.3135 | + | 23.2495i | −0.473947 | + | 0.894874i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.0205i | 0.731018i | 0.930808 | + | 0.365509i | \(0.119105\pi\) | ||||
−0.930808 | + | 0.365509i | \(0.880895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0533 | −0.462564 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.1256 | 1.30769 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.4947i | − | 0.669415i | −0.942322 | − | 0.334707i | \(-0.891363\pi\) | ||
0.942322 | − | 0.334707i | \(-0.108637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.19779 | + | 32.9939i | −0.313222 | + | 1.26063i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.4657i | 1.54386i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5236 | −0.400917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3090 | −0.620423 | −0.310211 | − | 0.950668i | \(-0.600400\pi\) | ||||
−0.310211 | + | 0.950668i | \(0.600400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.11733i | − | 0.0424437i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.60197 | + | 1.39189i | 0.212495 | + | 0.0527973i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 26.5236i | − | 1.00465i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2039 | −0.877653 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9672 | −0.489764 | −0.244882 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244882 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 18.7838i | − | 0.708444i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.7587 | − | 4.41241i | −0.668832 | − | 0.166181i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.08661i | 0.228911i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.36069 | −0.276437 | −0.138218 | − | 0.990402i | \(-0.544138\pi\) | ||||
−0.138218 | + | 0.990402i | \(0.544138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.993857 | 0.0372725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.40787i | 0.239977i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.5236 | − | 74.5523i | 0.692743 | − | 2.78810i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 14.3012i | − | 0.534089i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3197 | −0.720502 | −0.360251 | − | 0.932856i | \(-0.617309\pi\) | ||||
−0.360251 | + | 0.932856i | \(0.617309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.6369 | 1.58788 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9483i | 0.630313i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.83710 | + | 4.68035i | 0.328202 | + | 0.173824i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.1545i | − | 0.784577i | −0.919842 | − | 0.392288i | \(-0.871684\pi\) | ||
0.919842 | − | 0.392288i | \(-0.128316\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.6681 | −1.02474 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.2039 | 0.562338 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7526i | 0.840386i | 0.907435 | + | 0.420193i | \(0.138038\pi\) | ||||
−0.907435 | + | 0.420193i | \(0.861962\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0722347 | − | 0.290725i | 0.00266442 | − | 0.0107235i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.6225i | 1.57002i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.4534 | −1.04668 | −0.523338 | − | 0.852125i | \(-0.675314\pi\) | ||||
−0.523338 | + | 0.852125i | \(0.675314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.3484 | 1.29856 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.79380i | − | 0.139181i | −0.997576 | − | 0.0695904i | \(-0.977831\pi\) | ||
0.997576 | − | 0.0695904i | \(-0.0221692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.94214 | + | 0.979481i | 0.144429 | + | 0.0358854i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.17340i | − | 0.0429324i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.1773 | −1.50458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3607 | −0.633501 | −0.316750 | − | 0.948509i | \(-0.602592\pi\) | ||||
−0.316750 | + | 0.948509i | \(0.602592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 30.1112i | − | 1.09731i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.2039 | − | 2.78378i | −0.407753 | − | 0.101312i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.76487i | − | 0.173182i | −0.996244 | − | 0.0865910i | \(-0.972403\pi\) | ||
0.996244 | − | 0.0865910i | \(-0.0275973\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.6803 | −0.460267 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1978 | −0.514670 | −0.257335 | − | 0.966322i | \(-0.582844\pi\) | ||||
−0.257335 | + | 0.966322i | \(0.582844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.4657i | 1.17534i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.144469 | − | 0.581449i | 0.00522330 | − | 0.0210223i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.6803i | 0.746724i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.7091 | −1.97286 | −0.986430 | − | 0.164181i | \(-0.947502\pi\) | ||||
−0.986430 | + | 0.164181i | \(0.947502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.30122 | −0.226933 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0205i | 0.396381i | 0.980164 | + | 0.198190i | \(0.0635064\pi\) | ||||
−0.980164 | + | 0.198190i | \(0.936494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.6803 | + | 10.9528i | 0.742860 | + | 0.393437i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.8966i | 0.929034i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.3074 | 0.906731 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.3607 | 1.19374 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5236i | 0.376082i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.41855 | + | 29.8576i | −0.264779 | + | 1.06566i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.6925i | − | 1.20101i | −0.799622 | − | 0.600503i | \(-0.794967\pi\) | ||
0.799622 | − | 0.600503i | \(-0.205033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.183417 | 0.00652984 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.6270 | −0.875636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.8310i | 0.562174i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.15676 | + | 1.52973i | 0.218358 | + | 0.0542541i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.7009i | 0.839528i | 0.907633 | + | 0.419764i | \(0.137887\pi\) | ||||
−0.907633 | + | 0.419764i | \(0.862113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3668 | 0.579017 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.668060 | 0.0236047 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 73.5585i | 2.59582i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.81658 | − | 1.94214i | −0.275498 | − | 0.0684515i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.59374i | 0.232110i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.0349 | 1.16145 | 0.580723 | − | 0.814102i | \(-0.302770\pi\) | ||||
0.580723 | + | 0.814102i | \(0.302770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.26794 | −0.220097 | −0.110049 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110049 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 36.4202i | − | 1.27731i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.39189 | + | 13.6514i | −0.118813 | + | 0.478188i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5068i | 0.507528i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.30737 | 0.0456831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0616 | −0.525652 | −0.262826 | − | 0.964843i | \(-0.584655\pi\) | ||||
−0.262826 | + | 0.964843i | \(0.584655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5669i | 1.17007i | 0.811009 | + | 0.585034i | \(0.198919\pi\) | ||||
−0.811009 | + | 0.585034i | \(0.801081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.6742 | + | 40.9237i | −0.754599 | + | 1.42478i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.6576i | − | 0.370600i | −0.982682 | − | 0.185300i | \(-0.940674\pi\) | ||
0.982682 | − | 0.185300i | \(-0.0593256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.4846 | 1.82287 | 0.911433 | − | 0.411447i | \(-0.134977\pi\) | ||||
0.911433 | + | 0.411447i | \(0.134977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.47027 | −0.0856926 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.267938i | 0.00928351i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.09890 | − | 8.44748i | 0.0726353 | − | 0.292337i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.6270i | 0.851234i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.2101 | 0.628682 | 0.314341 | − | 0.949310i | \(-0.398217\pi\) | ||||
0.314341 | + | 0.949310i | \(0.398217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.2618i | 0.732295i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 59.0216 | + | 14.6647i | 2.03040 | + | 0.504483i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 48.3051i | − | 1.65978i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7526 | 0.369028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.88428 | −0.270270 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.7542i | 0.676371i | 0.941080 | + | 0.338185i | \(0.109813\pi\) | ||||
−0.941080 | + | 0.338185i | \(0.890187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.554787 | + | 0.137845i | 0.0189733 | + | 0.00471419i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.9939i | 1.67360i | 0.547510 | + | 0.836799i | \(0.315576\pi\) | ||||
−0.547510 | + | 0.836799i | \(0.684424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3090 | 0.829412 | 0.414706 | − | 0.909956i | \(-0.363885\pi\) | ||||
0.414706 | + | 0.909956i | \(0.363885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.8904 | −1.18906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 44.3584i | − | 1.50998i | −0.655737 | − | 0.754989i | \(-0.727642\pi\) | ||
0.655737 | − | 0.754989i | \(-0.272358\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.779243 | + | 3.13624i | −0.0264950 | + | 0.106635i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.08225i | 0.308449i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.7091 | 2.33080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.8720 | −1.68985 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.359084i | − | 0.0121531i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.6286 | + | 21.9071i | −0.663569 | + | 0.740594i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 37.9565i | − | 1.28170i | −0.767666 | − | 0.640850i | \(-0.778582\pi\) | ||
0.767666 | − | 0.640850i | \(-0.221418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.84324 | 0.0621711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0661 | 0.844498 | 0.422249 | − | 0.906480i | \(-0.361241\pi\) | ||||
0.422249 | + | 0.906480i | \(0.361241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 21.1278i | − | 0.711008i | −0.934675 | − | 0.355504i | \(-0.884309\pi\) | ||
0.934675 | − | 0.355504i | \(-0.115691\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.00614 | − | 12.0989i | 0.101050 | − | 0.406700i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 36.1894i | − | 1.21512i | −0.794274 | − | 0.607560i | \(-0.792148\pi\) | ||
0.794274 | − | 0.607560i | \(-0.207852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.13170 | −0.172112 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −47.4596 | −1.58996 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.6163i | 0.522581i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.9155 | − | 6.43907i | −0.866259 | − | 0.215234i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 14.8371i | − | 0.495396i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.36069 | 0.312197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.67420 | −0.189035 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 20.0000i | − | 0.665558i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.3340 | + | 8.28231i | 1.10806 | + | 0.275313i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2678i | 1.17105i | 0.810656 | + | 0.585523i | \(0.199111\pi\) | ||||
−0.810656 | + | 0.585523i | \(0.800889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.181328 | −0.00601426 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0061 | 0.497176 | 0.248588 | − | 0.968609i | \(-0.420034\pi\) | ||||
0.248588 | + | 0.968609i | \(0.420034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 81.1215i | − | 2.68473i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.30122 | − | 9.26180i | 0.0760761 | − | 0.306186i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.9770i | 1.35318i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.8781 | 1.08455 | 0.542275 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542275 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.1194 | −1.42083 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.0349i | 1.28485i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4764 | + | 25.4452i | −0.443102 | + | 0.836633i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.27021i | 0.0417190i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.2290 | 0.991781 | 0.495890 | − | 0.868385i | \(-0.334842\pi\) | ||||
0.495890 | + | 0.868385i | \(0.334842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.255652 | −0.00837866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.1978i | 1.05411i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.98771 | − | 40.1978i | 0.326633 | − | 1.31461i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.4124i | − | 0.928193i | −0.885785 | − | 0.464096i | \(-0.846379\pi\) | ||
0.885785 | − | 0.464096i | \(-0.153621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.9877 | −0.848077 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0821 | −1.37184 | −0.685918 | − | 0.727679i | \(-0.740599\pi\) | ||||
−0.685918 | + | 0.727679i | \(0.740599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.6225i | − | 0.345916i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30.0410 | − | 7.46412i | −0.977235 | − | 0.242808i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.2739i | 0.723805i | 0.932216 | + | 0.361902i | \(0.117873\pi\) | ||||
−0.932216 | + | 0.361902i | \(0.882127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −86.0698 | −2.79394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.8248 | −0.934709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6681i | 0.475145i | 0.971370 | + | 0.237573i | \(0.0763517\pi\) | ||||
−0.971370 | + | 0.237573i | \(0.923648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.0349 | + | 13.6742i | 1.78089 | + | 0.442487i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.5236i | 0.598783i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0000 | −1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09436 | −0.293367 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.22672i | − | 0.0395306i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.47027 | − | 9.94214i | 0.0795207 | − | 0.320049i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.403997i | 0.0129917i | 0.999979 | + | 0.00649584i | \(0.00206770\pi\) | ||||
−0.999979 | + | 0.00649584i | \(0.997932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.0595 | 0.612278 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.8326 | −1.50293 | −0.751464 | − | 0.659774i | \(-0.770652\pi\) | ||||
−0.751464 | + | 0.659774i | \(0.770652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.79153i | 0.217726i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −47.8843 | − | 25.3607i | −1.53352 | − | 0.812192i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.6041i | 1.71495i | 0.514529 | + | 0.857473i | \(0.327967\pi\) | ||||
−0.514529 | + | 0.857473i | \(0.672033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.1855 | 1.47610 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.967195 | −0.0308802 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 19.9916i | − | 0.637633i | −0.947817 | − | 0.318816i | \(-0.896715\pi\) | ||
0.947817 | − | 0.318816i | \(-0.103285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.09275 | + | 36.5958i | −0.289719 | + | 1.16604i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 21.5297i | − | 0.685299i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.08906 | 0.193621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.6270 | 0.782303 | 0.391152 | − | 0.920326i | \(-0.372077\pi\) | ||||
0.391152 | + | 0.920326i | \(0.372077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.2967i | 1.27878i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3607 | + | 5.30737i | 0.677179 | + | 0.168255i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 20.9795i | − | 0.664427i | −0.943204 | − | 0.332213i | \(-0.892205\pi\) | ||
0.943204 | − | 0.332213i | \(-0.107795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.3012 | −0.958688 |
(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 | 640.2.c.b.129.5 | yes | 6 | |
4.3 | odd | 2 | 640.2.c.a.129.2 | ✓ | 6 | ||
5.2 | odd | 4 | 3200.2.a.br.1.3 | 3 | |||
5.3 | odd | 4 | 3200.2.a.bt.1.1 | 3 | |||
5.4 | even | 2 | inner | 640.2.c.b.129.2 | yes | 6 | |
8.3 | odd | 2 | 640.2.c.d.129.5 | yes | 6 | ||
8.5 | even | 2 | 640.2.c.c.129.2 | yes | 6 | ||
16.3 | odd | 4 | 1280.2.f.i.129.6 | 6 | |||
16.5 | even | 4 | 1280.2.f.j.129.5 | 6 | |||
16.11 | odd | 4 | 1280.2.f.l.129.1 | 6 | |||
16.13 | even | 4 | 1280.2.f.k.129.2 | 6 | |||
20.3 | even | 4 | 3200.2.a.bq.1.3 | 3 | |||
20.7 | even | 4 | 3200.2.a.bs.1.1 | 3 | |||
20.19 | odd | 2 | 640.2.c.a.129.5 | yes | 6 | ||
40.3 | even | 4 | 3200.2.a.bv.1.1 | 3 | |||
40.13 | odd | 4 | 3200.2.a.bo.1.3 | 3 | |||
40.19 | odd | 2 | 640.2.c.d.129.2 | yes | 6 | ||
40.27 | even | 4 | 3200.2.a.bp.1.3 | 3 | |||
40.29 | even | 2 | 640.2.c.c.129.5 | yes | 6 | ||
40.37 | odd | 4 | 3200.2.a.bu.1.1 | 3 | |||
80.19 | odd | 4 | 1280.2.f.l.129.2 | 6 | |||
80.29 | even | 4 | 1280.2.f.j.129.6 | 6 | |||
80.59 | odd | 4 | 1280.2.f.i.129.5 | 6 | |||
80.69 | even | 4 | 1280.2.f.k.129.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.2 | ✓ | 6 | 4.3 | odd | 2 | ||
640.2.c.a.129.5 | yes | 6 | 20.19 | odd | 2 | ||
640.2.c.b.129.2 | yes | 6 | 5.4 | even | 2 | inner | |
640.2.c.b.129.5 | yes | 6 | 1.1 | even | 1 | trivial | |
640.2.c.c.129.2 | yes | 6 | 8.5 | even | 2 | ||
640.2.c.c.129.5 | yes | 6 | 40.29 | even | 2 | ||
640.2.c.d.129.2 | yes | 6 | 40.19 | odd | 2 | ||
640.2.c.d.129.5 | yes | 6 | 8.3 | odd | 2 | ||
1280.2.f.i.129.5 | 6 | 80.59 | odd | 4 | |||
1280.2.f.i.129.6 | 6 | 16.3 | odd | 4 | |||
1280.2.f.j.129.5 | 6 | 16.5 | even | 4 | |||
1280.2.f.j.129.6 | 6 | 80.29 | even | 4 | |||
1280.2.f.k.129.1 | 6 | 80.69 | even | 4 | |||
1280.2.f.k.129.2 | 6 | 16.13 | even | 4 | |||
1280.2.f.l.129.1 | 6 | 16.11 | odd | 4 | |||
1280.2.f.l.129.2 | 6 | 80.19 | odd | 4 | |||
3200.2.a.bo.1.3 | 3 | 40.13 | odd | 4 | |||
3200.2.a.bp.1.3 | 3 | 40.27 | even | 4 | |||
3200.2.a.bq.1.3 | 3 | 20.3 | even | 4 | |||
3200.2.a.br.1.3 | 3 | 5.2 | odd | 4 | |||
3200.2.a.bs.1.1 | 3 | 20.7 | even | 4 | |||
3200.2.a.bt.1.1 | 3 | 5.3 | odd | 4 | |||
3200.2.a.bu.1.1 | 3 | 40.37 | odd | 4 | |||
3200.2.a.bv.1.1 | 3 | 40.3 | even | 4 |