Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,2,Mod(73,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.bo (of order \(9\), degree \(6\), 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: | \(5.46176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 613.1 | ||
Root | \(2.42841 + 4.20614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.613 |
Dual form | 684.2.bo.e.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{8}{9}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.54690 | − | 2.13710i | −1.13901 | − | 0.955741i | −0.139602 | − | 0.990208i | \(-0.544582\pi\) |
−0.999406 | + | 0.0344670i | \(0.989027\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.596313 | − | 1.03284i | −0.225385 | − | 0.390379i | 0.731050 | − | 0.682324i | \(-0.239031\pi\) |
−0.956435 | + | 0.291946i | \(0.905697\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.647560 | − | 1.12161i | 0.195247 | − | 0.338177i | −0.751735 | − | 0.659466i | \(-0.770783\pi\) |
0.946981 | + | 0.321288i | \(0.104116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.496083 | + | 2.81343i | 0.137589 | + | 0.780304i | 0.973022 | + | 0.230712i | \(0.0741056\pi\) |
−0.835433 | + | 0.549592i | \(0.814783\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.08503 | + | 0.758891i | −0.505695 | + | 0.184058i | −0.582254 | − | 0.813007i | \(-0.697829\pi\) |
0.0765586 | + | 0.997065i | \(0.475607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.84913 | + | 3.29886i | −0.653635 | + | 0.756810i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.07384 | + | 5.09656i | −1.26648 | + | 1.06271i | −0.271524 | + | 0.962432i | \(0.587528\pi\) |
−0.994960 | + | 0.100275i | \(0.968028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.05125 | + | 5.96192i | 0.210249 | + | 1.19238i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.21893 | − | 1.53557i | −0.783436 | − | 0.285148i | −0.0808315 | − | 0.996728i | \(-0.525758\pi\) |
−0.702605 | + | 0.711580i | \(0.747980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.91714 | − | 6.78468i | −0.703538 | − | 1.21856i | −0.967216 | − | 0.253953i | \(-0.918269\pi\) |
0.263678 | − | 0.964611i | \(-0.415064\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.688545 | + | 3.90493i | −0.116385 | + | 0.660054i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.86729 | −1.29337 | −0.646687 | − | 0.762755i | \(-0.723846\pi\) | ||||
−0.646687 | + | 0.762755i | \(0.723846\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.40006 | + | 7.94015i | −0.218653 | + | 1.24004i | 0.655801 | + | 0.754934i | \(0.272331\pi\) |
−0.874454 | + | 0.485109i | \(0.838780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.37037 | − | 1.14988i | −0.208980 | − | 0.175355i | 0.532290 | − | 0.846562i | \(-0.321332\pi\) |
−0.741270 | + | 0.671207i | \(0.765776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.36453 | + | 1.95253i | 0.782497 | + | 0.284806i | 0.702213 | − | 0.711967i | \(-0.252195\pi\) |
0.0802834 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.78882 | − | 4.83038i | 0.398403 | − | 0.690054i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.83597 | − | 4.05786i | 0.664272 | − | 0.557390i | −0.247092 | − | 0.968992i | \(-0.579475\pi\) |
0.911364 | + | 0.411602i | \(0.135031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.04626 | + | 1.47272i | −0.545598 | + | 0.198581i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.41778 | + | 2.69985i | −0.965713 | + | 0.351491i | −0.776270 | − | 0.630401i | \(-0.782891\pi\) |
−0.189443 | + | 0.981892i | \(0.560668\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2096 | − | 9.40599i | 1.43524 | − | 1.20431i | 0.492715 | − | 0.870190i | \(-0.336004\pi\) |
0.942529 | − | 0.334123i | \(-0.108440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.74910 | − | 8.22569i | 0.589054 | − | 1.02027i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.30894 | − | 1.56833i | −0.526421 | − | 0.191601i | 0.0651188 | − | 0.997878i | \(-0.479257\pi\) |
−0.591539 | + | 0.806276i | \(0.701480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.20234 | − | 2.68708i | −0.380048 | − | 0.318898i | 0.432674 | − | 0.901551i | \(-0.357570\pi\) |
−0.812721 | + | 0.582653i | \(0.802015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.338056 | − | 1.91721i | 0.0395665 | − | 0.224393i | −0.958613 | − | 0.284714i | \(-0.908101\pi\) |
0.998179 | + | 0.0603212i | \(0.0192125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.54460 | −0.176023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.07749 | + | 6.11077i | −0.121227 | + | 0.687515i | 0.862250 | + | 0.506483i | \(0.169055\pi\) |
−0.983477 | + | 0.181032i | \(0.942056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.91858 | + | 6.78719i | 0.430120 | + | 0.744990i | 0.996883 | − | 0.0788906i | \(-0.0251378\pi\) |
−0.566763 | + | 0.823881i | \(0.691804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.93220 | + | 2.52311i | 0.751902 | + | 0.273670i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.743166 | + | 4.21470i | 0.0787754 | + | 0.446758i | 0.998527 | + | 0.0542567i | \(0.0172789\pi\) |
−0.919752 | + | 0.392501i | \(0.871610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.61001 | − | 2.19006i | 0.273604 | − | 0.229581i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.3064 | − | 2.31298i | 1.46781 | − | 0.237307i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.38339 | − | 0.867483i | 0.241997 | − | 0.0880795i | −0.218175 | − | 0.975910i | \(-0.570010\pi\) |
0.460171 | + | 0.887830i | \(0.347788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.16648 | − | 12.2867i | −0.215573 | − | 1.22257i | −0.879910 | − | 0.475141i | \(-0.842397\pi\) |
0.664337 | − | 0.747434i | \(-0.268714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.78891 | + | 15.2228i | −0.865997 | + | 1.49995i | 5.70163e−5 | 1.00000i | \(0.499982\pi\) | |
−0.866054 | + | 0.499951i | \(0.833351\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.35879 | − | 7.54965i | −0.421381 | − | 0.729853i | 0.574694 | − | 0.818368i | \(-0.305121\pi\) |
−0.996075 | + | 0.0885157i | \(0.971788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9617 | − | 12.5544i | −1.43307 | − | 1.20249i | −0.943869 | − | 0.330321i | \(-0.892843\pi\) |
−0.489204 | − | 0.872170i | \(-0.662713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.595683 | −0.0560372 | −0.0280186 | − | 0.999607i | \(-0.508920\pi\) | ||||
−0.0280186 | + | 0.999607i | \(0.508920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.3613 | 2.45821 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.02715 | + | 1.70098i | 0.185829 | + | 0.155929i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.66133 | + | 8.07366i | 0.423757 | + | 0.733969i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.75196 | − | 3.03448i | 0.156700 | − | 0.271412i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.69849 | + | 9.63264i | 0.150717 | + | 0.854758i | 0.962598 | + | 0.270935i | \(0.0873328\pi\) |
−0.811881 | + | 0.583823i | \(0.801556\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7025 | + | 5.35127i | −1.28456 | + | 0.467543i | −0.891939 | − | 0.452156i | \(-0.850655\pi\) |
−0.392624 | + | 0.919699i | \(0.628433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.10618 | + | 0.975555i | 0.442762 | + | 0.0845913i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8578 | − | 9.94991i | 1.01308 | − | 0.850078i | 0.0243410 | − | 0.999704i | \(-0.492251\pi\) |
0.988743 | + | 0.149625i | \(0.0478068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00473 | + | 11.3694i | 0.170039 | + | 0.964338i | 0.943716 | + | 0.330758i | \(0.107304\pi\) |
−0.773677 | + | 0.633580i | \(0.781585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.47680 | + | 1.26545i | 0.290745 | + | 0.105823i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.46353 | + | 12.9272i | 0.619813 | + | 1.07355i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.05008 | − | 22.9691i | 0.331795 | − | 1.88170i | −0.125040 | − | 0.992152i | \(-0.539906\pi\) |
0.456835 | − | 0.889552i | \(-0.348983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.39770 | −0.276501 | −0.138250 | − | 0.990397i | \(-0.544148\pi\) | ||||
−0.138250 | + | 0.990397i | \(0.544148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.52300 | + | 25.6512i | −0.363296 | + | 2.06035i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4382 | − | 14.6324i | −1.39172 | − | 1.16779i | −0.964638 | − | 0.263580i | \(-0.915097\pi\) |
−0.427083 | − | 0.904213i | \(-0.640459\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.88587 | + | 3.23419i | 0.700305 | + | 0.254890i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.53627 | − | 11.3211i | 0.511960 | − | 0.886741i | −0.487944 | − | 0.872875i | \(-0.662253\pi\) |
0.999904 | − | 0.0138657i | \(-0.00441372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6216 | − | 9.75170i | 0.899308 | − | 0.754609i | −0.0707468 | − | 0.997494i | \(-0.522538\pi\) |
0.970055 | + | 0.242885i | \(0.0780938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.54673 | − | 1.65488i | 0.349749 | − | 0.127298i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.6934 | − | 5.71194i | 1.19315 | − | 0.434271i | 0.332321 | − | 0.943167i | \(-0.392168\pi\) |
0.860828 | + | 0.508896i | \(0.169946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.53086 | − | 4.64095i | 0.418094 | − | 0.350823i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.84712 | − | 11.8596i | 0.511778 | − | 0.886425i | −0.488129 | − | 0.872771i | \(-0.662321\pi\) |
0.999907 | − | 0.0136533i | \(-0.00434612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.1404 | − | 6.96652i | −1.42269 | − | 0.517817i | −0.487864 | − | 0.872920i | \(-0.662224\pi\) |
−0.934827 | + | 0.355102i | \(0.884446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0372 | + | 16.8132i | 1.47316 | + | 1.23613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.499009 | + | 2.83002i | −0.0364911 | + | 0.206951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2065 | −1.53445 | −0.767224 | − | 0.641380i | \(-0.778362\pi\) | ||||
−0.767224 | + | 0.641380i | \(0.778362\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.43434 | − | 13.8059i | 0.175228 | − | 0.993767i | −0.762653 | − | 0.646808i | \(-0.776103\pi\) |
0.937880 | − | 0.346958i | \(-0.112786\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.84138 | + | 4.92142i | 0.202440 | + | 0.350637i | 0.949314 | − | 0.314329i | \(-0.101780\pi\) |
−0.746874 | + | 0.664966i | \(0.768446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0943 | − | 3.67403i | −0.715567 | − | 0.260445i | −0.0415244 | − | 0.999137i | \(-0.513221\pi\) |
−0.674043 | + | 0.738692i | \(0.735444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.929804 | + | 5.27318i | 0.0652595 | + | 0.370105i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.5347 | − | 17.2307i | 1.43421 | − | 1.20344i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.85504 | + | 5.33181i | 0.128316 | + | 0.368809i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9123 | − | 6.88351i | 1.30198 | − | 0.473880i | 0.404336 | − | 0.914610i | \(-0.367503\pi\) |
0.897640 | + | 0.440730i | \(0.145280\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.03279 | + | 5.85725i | 0.0704357 | + | 0.399461i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.67168 | + | 8.09159i | −0.317134 | + | 0.549293i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.16943 | − | 5.48962i | −0.213199 | − | 0.369272i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.60127 | + | 2.18272i | 0.174194 | + | 0.146166i | 0.725716 | − | 0.687994i | \(-0.241508\pi\) |
−0.551523 | + | 0.834160i | \(0.685953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7293 | −0.778503 | −0.389251 | − | 0.921132i | \(-0.627266\pi\) | ||||
−0.389251 | + | 0.921132i | \(0.627266\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.83401 | 0.517686 | 0.258843 | − | 0.965919i | \(-0.416659\pi\) | ||||
0.258843 | + | 0.965919i | \(0.416659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.10168 | + | 1.76352i | 0.137685 | + | 0.115532i | 0.709029 | − | 0.705179i | \(-0.249133\pi\) |
−0.571344 | + | 0.820711i | \(0.693578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.49015 | − | 16.4374i | −0.619069 | − | 1.07226i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.54354 | − | 14.7978i | 0.552636 | − | 0.957193i | −0.445448 | − | 0.895308i | \(-0.646955\pi\) |
0.998083 | − | 0.0618851i | \(-0.0197112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.561919 | + | 3.18680i | 0.0361964 | + | 0.205280i | 0.997543 | − | 0.0700625i | \(-0.0223199\pi\) |
−0.961346 | + | 0.275342i | \(0.911209\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.4259 | + | 6.34249i | −1.11330 | + | 0.405207i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6945 | − | 6.37931i | −0.680475 | − | 0.405906i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.06837 | + | 4.25287i | −0.319913 | + | 0.268439i | −0.788575 | − | 0.614939i | \(-0.789181\pi\) |
0.468662 | + | 0.883378i | \(0.344736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.78316 | + | 10.1128i | 0.112106 | + | 0.635786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6959 | + | 4.98492i | 0.854330 | + | 0.310951i | 0.731804 | − | 0.681515i | \(-0.238678\pi\) |
0.122525 | + | 0.992465i | \(0.460901\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.69137 | + | 8.12569i | 0.291507 | + | 0.504906i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.70600 | + | 9.67520i | −0.105196 | + | 0.596598i | 0.885945 | + | 0.463790i | \(0.153511\pi\) |
−0.991142 | + | 0.132809i | \(0.957600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.9888 | −1.28933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.75753 | + | 21.3100i | −0.229101 | + | 1.29929i | 0.625588 | + | 0.780154i | \(0.284859\pi\) |
−0.854689 | + | 0.519141i | \(0.826252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.66583 | − | 3.91509i | −0.283429 | − | 0.237825i | 0.489978 | − | 0.871735i | \(-0.337005\pi\) |
−0.773407 | + | 0.633910i | \(0.781449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.36768 | + | 2.68162i | 0.444288 | + | 0.161708i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.11381 | + | 14.0535i | −0.487512 | + | 0.844395i | −0.999897 | − | 0.0143607i | \(-0.995429\pi\) |
0.512385 | + | 0.858756i | \(0.328762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.15528 | + | 2.64760i | −0.188228 | + | 0.157942i | −0.732032 | − | 0.681270i | \(-0.761428\pi\) |
0.543804 | + | 0.839212i | \(0.316984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.3540 | + | 9.22811i | −1.50714 | + | 0.548554i | −0.957898 | − | 0.287109i | \(-0.907306\pi\) |
−0.549242 | + | 0.835663i | \(0.685084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.03582 | − | 3.28877i | 0.533367 | − | 0.194130i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.25130 | + | 7.76276i | −0.544194 | + | 0.456633i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.12397 | − | 5.41088i | 0.182504 | − | 0.316107i | −0.760228 | − | 0.649656i | \(-0.774913\pi\) |
0.942733 | + | 0.333549i | \(0.108246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.6622 | + | 8.97630i | 1.43589 | + | 0.522621i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3519 | − | 14.5600i | −1.00349 | − | 0.842026i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.370475 | + | 2.10107i | −0.0213538 | + | 0.121104i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −48.6513 | −2.78577 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.08041 | + | 11.7986i | −0.118735 | + | 0.673381i | 0.866098 | + | 0.499875i | \(0.166621\pi\) |
−0.984833 | + | 0.173506i | \(0.944490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.54108 | − | 7.86538i | −0.257501 | − | 0.446005i | 0.708071 | − | 0.706141i | \(-0.249566\pi\) |
−0.965572 | + | 0.260137i | \(0.916232\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5136 | + | 5.64648i | 0.876878 | + | 0.319158i | 0.740949 | − | 0.671561i | \(-0.234376\pi\) |
0.135929 | + | 0.990719i | \(0.456598\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.37258 | − | 19.1269i | −0.189423 | − | 1.07427i | −0.920139 | − | 0.391591i | \(-0.871925\pi\) |
0.730716 | − | 0.682681i | \(-0.239186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.45432 | + | 3.73762i | −0.249394 | + | 0.209266i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.43706 | − | 9.04041i | 0.191243 | − | 0.503022i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.2519 | + | 5.91521i | −0.901494 | + | 0.328117i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.18228 | − | 6.70504i | −0.0651812 | − | 0.369661i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.48454 | − | 12.9636i | 0.411387 | − | 0.712544i | −0.583654 | − | 0.812002i | \(-0.698378\pi\) |
0.995042 | + | 0.0994585i | \(0.0317110\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.62276 | + | 13.2030i | 0.416476 | + | 0.721357i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3718 | + | 10.3812i | 0.673934 | + | 0.565498i | 0.914227 | − | 0.405203i | \(-0.132799\pi\) |
−0.240293 | + | 0.970700i | \(0.577243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.1463 | −0.549454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0004 | −0.809947 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.3637 | − | 20.4436i | −1.30791 | − | 1.09747i | −0.988719 | − | 0.149780i | \(-0.952143\pi\) |
−0.319194 | − | 0.947689i | \(-0.603412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.77710 | + | 3.07803i | 0.0951261 | + | 0.164763i | 0.909661 | − | 0.415351i | \(-0.136341\pi\) |
−0.814535 | + | 0.580114i | \(0.803008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7010 | + | 27.1949i | −0.835678 | + | 1.44744i | 0.0577986 | + | 0.998328i | \(0.481592\pi\) |
−0.893477 | + | 0.449109i | \(0.851741\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.41347 | + | 13.6874i | 0.128093 | + | 0.726454i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.9000 | + | 5.78713i | −0.839171 | + | 0.305433i | −0.725617 | − | 0.688099i | \(-0.758446\pi\) |
−0.113554 | + | 0.993532i | \(0.536223\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.76493 | − | 18.7977i | −0.145523 | − | 0.989355i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.95827 | + | 4.16048i | −0.259528 | + | 0.217770i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.65004 | + | 9.35784i | 0.0861314 | + | 0.488475i | 0.997107 | + | 0.0760144i | \(0.0242195\pi\) |
−0.910975 | + | 0.412461i | \(0.864669\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.07490 | − | 2.57505i | −0.367310 | − | 0.133690i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6964 | + | 20.2588i | 0.605619 | + | 1.04896i | 0.991953 | + | 0.126604i | \(0.0404078\pi\) |
−0.386334 | + | 0.922359i | \(0.626259\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.22726 | − | 12.6314i | 0.114710 | − | 0.650552i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.1013 | −1.13527 | −0.567634 | − | 0.823281i | \(-0.692141\pi\) | ||||
−0.567634 | + | 0.823281i | \(0.692141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.13998 | + | 17.8077i | −0.160446 | + | 0.909932i | 0.793191 | + | 0.608973i | \(0.208418\pi\) |
−0.953637 | + | 0.300960i | \(0.902693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.93393 | + | 3.30096i | 0.200492 | + | 0.168232i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.8516 | + | 11.5930i | 1.61494 | + | 0.587791i | 0.982409 | − | 0.186742i | \(-0.0597929\pi\) |
0.632533 | + | 0.774533i | \(0.282015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.79644 | − | 15.2359i | 0.444855 | − | 0.770512i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.8036 | − | 13.2608i | 0.795165 | − | 0.667223i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4034 | − | 5.97033i | 0.823261 | − | 0.299642i | 0.104171 | − | 0.994559i | \(-0.466781\pi\) |
0.719090 | + | 0.694917i | \(0.244559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.9170 | + | 11.2529i | −1.54392 | + | 0.561941i | −0.966981 | − | 0.254847i | \(-0.917975\pi\) |
−0.576938 | + | 0.816788i | \(0.695753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.1450 | − | 14.3863i | 0.854052 | − | 0.716634i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.09455 | + | 8.82401i | −0.252527 | + | 0.437390i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.26825 | − | 2.64543i | −0.359392 | − | 0.130808i | 0.156013 | − | 0.987755i | \(-0.450136\pi\) |
−0.515404 | + | 0.856947i | \(0.672358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.21185 | + | 6.05146i | 0.354872 | + | 0.297773i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.52467 | − | 25.6607i | 0.222107 | − | 1.25963i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.4903 | 1.29414 | 0.647068 | − | 0.762432i | \(-0.275995\pi\) | ||||
0.647068 | + | 0.762432i | \(0.275995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.83547 | − | 10.4095i | 0.0894554 | − | 0.507327i | −0.906851 | − | 0.421452i | \(-0.861520\pi\) |
0.996306 | − | 0.0858746i | \(-0.0273684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.71633 | − | 11.6330i | −0.325790 | − | 0.564285i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3994 | − | 5.96888i | −0.793621 | − | 0.288855i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.61415 | − | 14.8256i | −0.125919 | − | 0.714123i | −0.980758 | − | 0.195229i | \(-0.937455\pi\) |
0.854838 | − | 0.518894i | \(-0.173656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.7556 | + | 24.9679i | −1.42996 | + | 1.19988i | −0.484228 | + | 0.874942i | \(0.660899\pi\) |
−0.945735 | + | 0.324939i | \(0.894656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.492330 | − | 34.5575i | 0.0235513 | − | 1.65311i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.955140 | + | 0.347643i | −0.0455864 | + | 0.0165921i | −0.364713 | − | 0.931120i | \(-0.618833\pi\) |
0.319126 | + | 0.947712i | \(0.396611\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.08139 | + | 11.8042i | 0.0988900 | + | 0.560833i | 0.993486 | + | 0.113957i | \(0.0363525\pi\) |
−0.894596 | + | 0.446876i | \(0.852536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.11448 | − | 12.3226i | 0.337259 | − | 0.584149i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7291 | + | 27.2436i | 0.742301 | + | 1.28570i | 0.951445 | + | 0.307818i | \(0.0995989\pi\) |
−0.209144 | + | 0.977885i | \(0.567068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.99910 | + | 6.71205i | 0.376663 | + | 0.316058i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3278 | −0.531056 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.25795 | −0.245956 | −0.122978 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122978 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.8528 | − | 10.7848i | −0.598616 | − | 0.502299i | 0.292384 | − | 0.956301i | \(-0.405551\pi\) |
−0.891001 | + | 0.454002i | \(0.849996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.73299 | − | 8.19777i | −0.219961 | − | 0.380983i | 0.734835 | − | 0.678246i | \(-0.237260\pi\) |
−0.954796 | + | 0.297263i | \(0.903926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.27914 | + | 16.0719i | −0.429387 | + | 0.743721i | −0.996819 | − | 0.0796999i | \(-0.974604\pi\) |
0.567432 | + | 0.823421i | \(0.307937\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.949640 | + | 5.38568i | 0.0438503 | + | 0.248687i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.17711 | + | 0.792404i | −0.100104 | + | 0.0364348i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.6627 | − | 13.5184i | −1.03983 | − | 0.620265i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.52763 | − | 4.63823i | 0.252564 | − | 0.211926i | −0.507712 | − | 0.861527i | \(-0.669508\pi\) |
0.760275 | + | 0.649601i | \(0.225064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.90283 | − | 22.1340i | −0.177954 | − | 1.00923i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.92415 | − | 2.88415i | −0.359817 | − | 0.130963i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.32705 | − | 4.03057i | −0.105449 | − | 0.182642i | 0.808473 | − | 0.588534i | \(-0.200295\pi\) |
−0.913921 | + | 0.405891i | \(0.866961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.690291 | + | 3.91483i | −0.0311524 | + | 0.176674i | −0.996414 | − | 0.0846112i | \(-0.973035\pi\) |
0.965262 | + | 0.261285i | \(0.0841463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.96195 | 0.448664 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.865741 | + | 4.90986i | −0.0388338 | + | 0.220237i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.215315 | + | 0.180670i | 0.00963881 | + | 0.00808792i | 0.647594 | − | 0.761985i | \(-0.275775\pi\) |
−0.637955 | + | 0.770073i | \(0.720220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.6506 | + | 12.6118i | 1.54499 | + | 0.562332i | 0.967237 | − | 0.253877i | \(-0.0817057\pi\) |
0.577757 | + | 0.816208i | \(0.303928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.7402 | + | 35.9230i | −0.922925 | + | 1.59855i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.9516 | + | 16.7413i | −0.884338 | + | 0.742047i | −0.967066 | − | 0.254525i | \(-0.918081\pi\) |
0.0827287 | + | 0.996572i | \(0.473636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.18177 | + | 0.794099i | −0.0965158 | + | 0.0351289i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 54.9172 | − | 19.9882i | 2.41994 | − | 0.880786i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.66383 | − | 4.75252i | 0.249095 | − | 0.209015i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.97112 | − | 8.61023i | 0.217789 | − | 0.377221i | −0.736343 | − | 0.676608i | \(-0.763449\pi\) |
0.954132 | + | 0.299387i | \(0.0967823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.3037 | + | 12.8495i | 1.54373 | + | 0.561870i | 0.966935 | − | 0.255022i | \(-0.0820829\pi\) |
0.576790 | + | 0.816892i | \(0.304305\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.3162 | + | 11.1736i | 0.580062 | + | 0.486730i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.92275 | − | 39.2608i | 0.300989 | − | 1.70699i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.0336 | −0.997695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.03297 | + | 28.5434i | −0.217594 | + | 1.23404i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.61186 | − | 6.25593i | −0.155574 | − | 0.269462i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.50545 | + | 0.911911i | 0.107718 | + | 0.0392061i | 0.395317 | − | 0.918545i | \(-0.370635\pi\) |
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2760 | + | 63.9494i | 0.483011 | + | 2.73929i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.5767 | + | 14.7486i | −0.751526 | + | 0.630605i | −0.935906 | − | 0.352250i | \(-0.885417\pi\) |
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.0859 | − | 9.54264i | 0.727884 | − | 0.406530i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.95400 | − | 2.53105i | 0.295714 | − | 0.107631i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.26779 | + | 7.18999i | 0.0537180 | + | 0.304650i | 0.999815 | − | 0.0192335i | \(-0.00612259\pi\) |
−0.946097 | + | 0.323883i | \(0.895011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.55528 | − | 4.42588i | 0.108077 | − | 0.187195i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1345 | + | 36.6060i | 0.890712 | + | 1.54276i | 0.839024 | + | 0.544094i | \(0.183127\pi\) |
0.0516876 | + | 0.998663i | \(0.483540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.51714 | + | 1.27304i | 0.0638268 | + | 0.0535570i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0782 | −0.632112 | −0.316056 | − | 0.948741i | \(-0.602359\pi\) | ||||
−0.316056 | + | 0.948741i | \(0.602359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.7731 | −1.79000 | −0.894998 | − | 0.446070i | \(-0.852823\pi\) | ||||
−0.894998 | + | 0.446070i | \(0.852823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −36.7704 | − | 30.8540i | −1.53343 | − | 1.28670i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6399 | − | 20.1609i | −0.484576 | − | 0.839311i | 0.515267 | − | 0.857030i | \(-0.327693\pi\) |
−0.999843 | + | 0.0177189i | \(0.994360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.67341 | − | 8.09458i | 0.193886 | − | 0.335820i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.41974 | − | 8.05177i | −0.0587998 | − | 0.333470i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.5574 | − | 7.48229i | 0.848496 | − | 0.308827i | 0.119069 | − | 0.992886i | \(-0.462009\pi\) |
0.729427 | + | 0.684059i | \(0.239787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.5421 | + | 6.40834i | 1.38208 | + | 0.264051i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1385 | − | 21.0937i | 1.03231 | − | 0.866213i | 0.0411885 | − | 0.999151i | \(-0.486886\pi\) |
0.991124 | + | 0.132938i | \(0.0424411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.52778 | − | 8.66445i | −0.0626327 | − | 0.355208i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.49512 | − | 2.36403i | −0.265384 | − | 0.0965917i | 0.205901 | − | 0.978573i | \(-0.433987\pi\) |
−0.471285 | + | 0.881981i | \(0.656210\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0005 | + | 29.4457i | 0.693465 | + | 1.20112i | 0.970696 | + | 0.240313i | \(0.0772500\pi\) |
−0.277231 | + | 0.960803i | \(0.589417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.38230 | − | 30.5245i | 0.218822 | − | 1.24100i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1493 | 0.858424 | 0.429212 | − | 0.903204i | \(-0.358791\pi\) | ||||
0.429212 | + | 0.903204i | \(0.358791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.83204 | + | 16.0613i | −0.114572 | + | 0.649772i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.92762 | − | 3.29566i | −0.158635 | − | 0.133111i | 0.560015 | − | 0.828482i | \(-0.310795\pi\) |
−0.718650 | + | 0.695372i | \(0.755240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.5654 | − | 9.30504i | −1.02922 | − | 0.374607i | −0.228439 | − | 0.973558i | \(-0.573362\pi\) |
−0.800785 | + | 0.598951i | \(0.795584\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.74222 | − | 9.94582i | 0.230799 | − | 0.399756i | −0.727244 | − | 0.686379i | \(-0.759199\pi\) |
0.958044 | + | 0.286623i | \(0.0925326\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.90997 | − | 3.28086i | 0.156650 | − | 0.131445i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.4969 | − | 6.36837i | 0.699878 | − | 0.254735i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.4036 | − | 5.97041i | 0.654053 | − | 0.238056i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.74578 | − | 2.30398i | 0.109308 | − | 0.0917201i | −0.586496 | − | 0.809952i | \(-0.699493\pi\) |
0.695803 | + | 0.718232i | \(0.255048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.2600 | − | 28.1632i | 0.645259 | − | 1.11762i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.9734 | + | 5.44987i | 0.593268 | + | 0.215932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.30991 | − | 2.77734i | −0.130734 | − | 0.109698i | 0.575076 | − | 0.818100i | \(-0.304972\pi\) |
−0.705810 | + | 0.708401i | \(0.749417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.16436 | + | 17.9460i | −0.124790 | + | 0.707720i | 0.856642 | + | 0.515911i | \(0.172547\pi\) |
−0.981432 | + | 0.191809i | \(0.938565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4490 | 1.03982 | 0.519910 | − | 0.854221i | \(-0.325966\pi\) | ||||
0.519910 | + | 0.854221i | \(0.325966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.77529 | + | 10.0682i | −0.0696862 | + | 0.395210i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.435379 | − | 0.754099i | −0.0170377 | − | 0.0295102i | 0.857381 | − | 0.514683i | \(-0.172090\pi\) |
−0.874419 | + | 0.485172i | \(0.838757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.8820 | + | 17.7916i | 1.90998 | + | 0.695175i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.71041 | − | 26.7141i | −0.183492 | − | 1.04063i | −0.927878 | − | 0.372884i | \(-0.878369\pi\) |
0.744387 | − | 0.667749i | \(-0.232742\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.42547 | − | 2.03521i | 0.0943398 | − | 0.0791605i | −0.594398 | − | 0.804171i | \(-0.702610\pi\) |
0.688738 | + | 0.725011i | \(0.258165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.9201 | − | 13.3971i | −0.423462 | − | 0.519516i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.4513 | − | 12.1753i | 1.29524 | − | 0.471428i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.29092 | − | 18.6637i | −0.127045 | − | 0.720506i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.92701 | − | 8.53384i | 0.189922 | − | 0.328955i | −0.755302 | − | 0.655377i | \(-0.772510\pi\) |
0.945224 | + | 0.326422i | \(0.105843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.247613 | + | 0.428878i | 0.00951653 | + | 0.0164831i | 0.870744 | − | 0.491736i | \(-0.163637\pi\) |
−0.861228 | + | 0.508219i | \(0.830304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.31722 | − | 1.94438i | −0.0889268 | − | 0.0746185i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.8365 | −0.452910 | −0.226455 | − | 0.974022i | \(-0.572714\pi\) | ||||
−0.226455 | + | 0.974022i | \(0.572714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.4647 | −1.96636 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8155 | + | 11.5926i | 0.526330 | + | 0.441643i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.11315 | + | 15.7844i | 0.346680 | + | 0.600468i | 0.985658 | − | 0.168758i | \(-0.0539755\pi\) |
−0.638977 | + | 0.769226i | \(0.720642\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.1917 | − | 33.2409i | 0.727982 | − | 1.26090i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.10652 | − | 17.6180i | −0.117668 | − | 0.667328i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.5323 | − | 5.65330i | 0.586648 | − | 0.213522i | −0.0316067 | − | 0.999500i | \(-0.510062\pi\) |
0.618254 | + | 0.785978i | \(0.287840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.4149 | − | 25.9531i | 0.845395 | − | 0.978839i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.3984 | + | 9.56438i | −0.428680 | + | 0.359705i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.27055 | − | 18.5482i | −0.122828 | − | 0.696593i | −0.982574 | − | 0.185871i | \(-0.940489\pi\) |
0.859746 | − | 0.510722i | \(-0.170622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.3706 | + | 21.2452i | 2.18600 | + | 0.795637i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.15066 | − | 10.6533i | −0.230022 | − | 0.398409i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.17486 | − | 35.0194i | 0.230283 | − | 1.30600i | −0.622039 | − | 0.782986i | \(-0.713696\pi\) |
0.852323 | − | 0.523016i | \(-0.175193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.9638 | 0.780732 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.71978 | − | 26.7672i | 0.175288 | − | 0.994109i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.02657 | − | 5.89599i | −0.260601 | − | 0.218670i | 0.503120 | − | 0.864216i | \(-0.332185\pi\) |
−0.763721 | + | 0.645546i | \(0.776630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.72990 | + | 1.35757i | 0.137955 | + | 0.0502117i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.77022 | + | 9.99431i | −0.213128 | + | 0.369148i | −0.952692 | − | 0.303938i | \(-0.901698\pi\) |
0.739564 | + | 0.673086i | \(0.235032\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.54934 | + | 3.81735i | −0.167577 | + | 0.140614i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.08882 | − | 3.30806i | 0.334338 | − | 0.121689i | −0.169396 | − | 0.985548i | \(-0.554182\pi\) |
0.503733 | + | 0.863859i | \(0.331959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.9925 | + | 8.00463i | −0.806828 | + | 0.293662i | −0.712313 | − | 0.701862i | \(-0.752352\pi\) |
−0.0945153 | + | 0.995523i | \(0.530130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −59.4025 | + | 49.8446i | −2.17634 | + | 1.82616i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.19841 | + | 9.00392i | −0.189946 | + | 0.328996i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.60159 | + | 0.946900i | 0.0949332 | + | 0.0345529i | 0.389050 | − | 0.921217i | \(-0.372803\pi\) |
−0.294117 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.65359 | + | 7.26123i | 0.314936 | + | 0.264263i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.87344 | + | 21.9673i | −0.140782 | + | 0.798417i | 0.829875 | + | 0.557950i | \(0.188412\pi\) |
−0.970657 | + | 0.240467i | \(0.922699\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.666605 | 0.0241644 | 0.0120822 | − | 0.999927i | \(-0.496154\pi\) | ||||
0.0120822 | + | 0.999927i | \(0.496154\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.04485 | + | 22.9395i | −0.146433 | + | 0.830464i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.2757 | − | 19.5300i | −0.407141 | − | 0.705189i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5010 | + | 6.73381i | 0.667162 | + | 0.242827i | 0.653326 | − | 0.757077i | \(-0.273373\pi\) |
0.0138367 | + | 0.999904i | \(0.495595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.57404 | + | 48.6258i | 0.308387 | + | 1.74895i | 0.607119 | + | 0.794611i | \(0.292325\pi\) |
−0.298733 | + | 0.954337i | \(0.596564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3318 | − | 30.4860i | 1.30508 | − | 1.09509i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.2045 | − | 27.2411i | −0.795558 | − | 0.976014i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.08756 | + | 1.85172i | −0.182047 | + | 0.0662597i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.1424 | + | 74.5344i | 0.469073 | + | 2.66025i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9273 | − | 36.2472i | 0.745978 | − | 1.29207i | −0.203759 | − | 0.979021i | \(-0.565316\pi\) |
0.949737 | − | 0.313050i | \(-0.101351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.355214 | + | 0.615248i | 0.0126300 | + | 0.0218757i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0240 | + | 26.8713i | 1.13720 | + | 0.954228i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.2358 | −1.77944 | −0.889722 | − | 0.456503i | \(-0.849102\pi\) | ||||
−0.889722 | + | 0.456503i | \(0.849102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6670 | −0.448126 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.93145 | − | 1.62068i | −0.0681593 | − | 0.0571925i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.7196 | − | 27.2272i | −0.554043 | − | 0.959631i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.91982 | − | 8.52138i | 0.172972 | − | 0.299596i | −0.766486 | − | 0.642261i | \(-0.777996\pi\) |
0.939458 | + | 0.342665i | \(0.111330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.97290 | − | 28.2027i | −0.174622 | − | 0.990331i | −0.938579 | − | 0.345064i | \(-0.887857\pi\) |
0.763957 | − | 0.645267i | \(-0.223254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.8416 | + | 14.8651i | −1.43062 | + | 0.520703i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.69765 | − | 1.24451i | 0.269307 | − | 0.0435399i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.3403 | − | 30.4931i | 1.26829 | − | 1.06422i | 0.273537 | − | 0.961861i | \(-0.411806\pi\) |
0.994748 | − | 0.102356i | \(-0.0326381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.04848 | + | 39.9739i | 0.245695 | + | 1.39340i | 0.818874 | + | 0.573974i | \(0.194599\pi\) |
−0.573179 | + | 0.819430i | \(0.694290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.74185 | − | 0.633981i | −0.0605700 | − | 0.0220457i | 0.311557 | − | 0.950227i | \(-0.399149\pi\) |
−0.372127 | + | 0.928182i | \(0.621372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4767 | + | 26.8065i | 0.537529 | + | 0.931028i | 0.999036 | + | 0.0438911i | \(0.0139755\pi\) |
−0.461507 | + | 0.887136i | \(0.652691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.14906 | + | 12.1879i | −0.0744605 | + | 0.422286i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.4395 | −1.74553 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.44892 | + | 30.9024i | −0.188118 | + | 1.06687i | 0.733766 | + | 0.679402i | \(0.237761\pi\) |
−0.921884 | + | 0.387466i | \(0.873350\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.77385 | − | 5.68394i | −0.233581 | − | 0.195998i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.1167 | − | 5.50203i | −0.520030 | − | 0.189276i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.55923 | − | 9.62886i | 0.191017 | − | 0.330852i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.7847 | − | 40.0961i | 1.63804 | − | 1.37448i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6764 | + | 9.70940i | −0.913381 | + | 0.332444i | −0.755602 | − | 0.655031i | \(-0.772656\pi\) |
−0.157779 | + | 0.987474i | \(0.550433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.11088 | + | 2.22418i | −0.208744 | + | 0.0759765i | −0.444276 | − | 0.895890i | \(-0.646539\pi\) |
0.235532 | + | 0.971867i | \(0.424317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5436 | + | 10.5253i | −0.427982 | + | 0.359119i | −0.831190 | − | 0.555989i | \(-0.812340\pi\) |
0.403208 | + | 0.915108i | \(0.367895\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.5642 | + | 42.5464i | −0.836174 | + | 1.44829i | 0.0568979 | + | 0.998380i | \(0.481879\pi\) |
−0.893071 | + | 0.449915i | \(0.851454\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.1765 | − | 18.9907i | −1.77406 | − | 0.645703i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.15614 | + | 5.16562i | 0.208833 | + | 0.175232i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.27478 | − | 12.9009i | 0.0770779 | − | 0.437130i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.17886 | −0.141271 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.24069 | + | 12.7076i | −0.0756628 | + | 0.429105i | 0.923321 | + | 0.384030i | \(0.125464\pi\) |
−0.998984 | + | 0.0450756i | \(0.985647\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.6390 | − | 32.2837i | −0.627965 | − | 1.08767i | −0.987960 | − | 0.154712i | \(-0.950555\pi\) |
0.359995 | − | 0.932954i | \(-0.382778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.29529 | − | 2.65527i | −0.245506 | − | 0.0893570i | 0.216336 | − | 0.976319i | \(-0.430589\pi\) |
−0.461842 | + | 0.886962i | \(0.652811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.14167 | + | 40.5024i | 0.239794 | + | 1.35994i | 0.832279 | + | 0.554357i | \(0.187036\pi\) |
−0.592485 | + | 0.805581i | \(0.701853\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.93618 | − | 7.49835i | 0.299710 | − | 0.251487i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.7253 | + | 12.1338i | −0.727011 | + | 0.406043i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.7840 | + | 15.5721i | −1.43011 | + | 0.520518i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.10781 | + | 34.6391i | 0.203707 | + | 1.15528i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.00369 | + | 12.1308i | −0.233327 | + | 0.404134i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.8604 | + | 58.6479i | 1.12556 | + | 1.94952i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5449 | − | 21.4347i | −0.848206 | − | 0.711729i | 0.111188 | − | 0.993799i | \(-0.464534\pi\) |
−0.959394 | + | 0.282070i | \(0.908979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6721 | −0.883687 | −0.441844 | − | 0.897092i | \(-0.645675\pi\) | ||||
−0.441844 | + | 0.897092i | \(0.645675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.1501 | 0.335919 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.2943 | + | 11.9944i | 0.472040 | + | 0.396089i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.49951 | + | 2.59722i | 0.0494642 | + | 0.0856745i | 0.889697 | − | 0.456551i | \(-0.150915\pi\) |
−0.840233 | + | 0.542225i | \(0.817582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.97128 | − | 10.3426i | 0.196547 | − | 0.340429i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.27047 | − | 46.9041i | −0.271931 | − | 1.54220i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.32189 | + | 2.30098i | −0.207415 | + | 0.0754927i | −0.443638 | − | 0.896206i | \(-0.646312\pi\) |
0.236224 | + | 0.971699i | \(0.424090\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.98903 | + | 22.9623i | 0.261830 | + | 0.752559i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.31896 | − | 6.14134i | 0.239356 | − | 0.200843i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.73192 | − | 15.4935i | −0.0892481 | − | 0.506151i | −0.996359 | − | 0.0852590i | \(-0.972828\pi\) |
0.907111 | − | 0.420892i | \(-0.138283\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.49945 | + | 1.63766i | 0.146678 | + | 0.0533864i | 0.414316 | − | 0.910133i | \(-0.364021\pi\) |
−0.267638 | + | 0.963520i | \(0.586243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.9637 | − | 55.3627i | −1.04088 | − | 1.80286i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.17749 | − | 29.3630i | 0.168246 | − | 0.954169i | −0.777409 | − | 0.628996i | \(-0.783466\pi\) |
0.945654 | − | 0.325173i | \(-0.105423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.56164 | 0.180538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.728873 | − | 4.13365i | 0.0236105 | − | 0.133902i | −0.970724 | − | 0.240197i | \(-0.922788\pi\) |
0.994335 | + | 0.106295i | \(0.0338989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.0108 | + | 45.3204i | 1.74775 | + | 1.46653i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.3477 | − | 6.31405i | −0.560187 | − | 0.203891i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1879 | + | 26.3062i | −0.489932 | + | 0.848588i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.7045 | + | 29.9597i | −1.14937 | + | 0.964435i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.76004 | + | 2.82442i | −0.249546 | + | 0.0908274i | −0.463765 | − | 0.885958i | \(-0.653502\pi\) |
0.214219 | + | 0.976786i | \(0.431279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.3878 | − | 4.14480i | 0.365450 | − | 0.133013i | −0.152767 | − | 0.988262i | \(-0.548818\pi\) |
0.518217 | + | 0.855249i | \(0.326596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5474 | − | 8.85028i | 0.338133 | − | 0.283727i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8156 | − | 25.6614i | 0.473994 | − | 0.820982i | −0.525562 | − | 0.850755i | \(-0.676145\pi\) |
0.999557 | + | 0.0297727i | \(0.00947834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.20849 | + | 1.89573i | 0.166464 | + | 0.0605879i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.4542 | − | 23.0368i | −0.875652 | − | 0.734759i | 0.0896287 | − | 0.995975i | \(-0.471432\pi\) |
−0.965280 | + | 0.261216i | \(0.915876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.28086 | − | 18.6067i | 0.104537 | − | 0.592858i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.1838 | 0.451020 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.48372 | + | 14.0859i | −0.0788980 | + | 0.447453i | 0.919609 | + | 0.392834i | \(0.128505\pi\) |
−0.998507 | + | 0.0546185i | \(0.982606\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.8574 | + | 30.9300i | 0.566118 | + | 0.980546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.44915 | + | 0.891419i | 0.0775654 | + | 0.0282315i | 0.380511 | − | 0.924776i | \(-0.375748\pi\) |
−0.302946 | + | 0.953008i | \(0.597970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.2.bo.e.613.1 | 12 | ||
3.2 | odd | 2 | 228.2.q.b.157.2 | yes | 12 | ||
12.11 | even | 2 | 912.2.bo.g.385.2 | 12 | |||
19.4 | even | 9 | inner | 684.2.bo.e.289.1 | 12 | ||
57.2 | even | 18 | 4332.2.a.u.1.5 | 6 | |||
57.17 | odd | 18 | 4332.2.a.t.1.5 | 6 | |||
57.23 | odd | 18 | 228.2.q.b.61.2 | ✓ | 12 | ||
228.23 | even | 18 | 912.2.bo.g.289.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.b.61.2 | ✓ | 12 | 57.23 | odd | 18 | ||
228.2.q.b.157.2 | yes | 12 | 3.2 | odd | 2 | ||
684.2.bo.e.289.1 | 12 | 19.4 | even | 9 | inner | ||
684.2.bo.e.613.1 | 12 | 1.1 | even | 1 | trivial | ||
912.2.bo.g.289.2 | 12 | 228.23 | even | 18 | |||
912.2.bo.g.385.2 | 12 | 12.11 | even | 2 | |||
4332.2.a.t.1.5 | 6 | 57.17 | odd | 18 | |||
4332.2.a.u.1.5 | 6 | 57.2 | even | 18 |