Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(209,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.k (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.6 | ||
Root | \(-0.420861 + 1.68014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.209 |
Dual form | 1680.2.k.e.209.5 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.420861 | + | 1.68014i | 0.242984 | + | 0.970030i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.95522 | − | 1.08495i | 0.874400 | − | 0.485206i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37608 | − | 1.16372i | −0.898073 | − | 0.439846i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.64575 | + | 1.41421i | −0.881917 | + | 0.471405i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.841723 | 0.233452 | 0.116726 | − | 0.993164i | \(-0.462760\pi\) | ||||
0.116726 | + | 0.993164i | \(0.462760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.64575 | + | 2.82843i | 0.683130 | + | 0.730297i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.19038i | − | 0.288709i | −0.989526 | − | 0.144354i | \(-0.953890\pi\) | ||
0.989526 | − | 0.144354i | \(-0.0461105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55066i | 1.04399i | 0.852948 | + | 0.521996i | \(0.174813\pi\) | ||||
−0.852948 | + | 0.521996i | \(0.825187\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.955218 | − | 4.48191i | 0.208446 | − | 0.978034i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.29150 | 0.686326 | 0.343163 | − | 0.939276i | \(-0.388502\pi\) | ||||
0.343163 | + | 0.939276i | \(0.388502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.64575 | − | 4.24264i | 0.529150 | − | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.48957 | − | 3.85005i | −0.671569 | − | 0.740942i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.98430i | 1.48265i | 0.671148 | + | 0.741323i | \(0.265802\pi\) | ||||
−0.671148 | + | 0.741323i | \(0.734198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.53019i | 0.993252i | 0.867965 | + | 0.496626i | \(0.165428\pi\) | ||||
−0.867965 | + | 0.496626i | \(0.834572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.75216 | + | 1.19038i | −0.827245 | + | 0.207218i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.90834 | + | 0.302606i | −0.998691 | + | 0.0511497i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.8127i | 1.77760i | 0.458294 | + | 0.888801i | \(0.348461\pi\) | ||||
−0.458294 | + | 0.888801i | \(0.651539\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.354249 | + | 1.41421i | 0.0567252 | + | 0.226455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.82087 | −1.22141 | −0.610707 | − | 0.791856i | \(-0.709115\pi\) | ||||
−0.610707 | + | 0.791856i | \(0.709115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.65489i | 0.709864i | 0.934892 | + | 0.354932i | \(0.115496\pi\) | ||||
−0.934892 | + | 0.354932i | \(0.884504\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.63866 | + | 5.63561i | −0.542420 | + | 0.840108i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.33981i | − | 0.633027i | −0.948588 | − | 0.316513i | \(-0.897488\pi\) | ||
0.948588 | − | 0.316513i | \(-0.102512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29150 | + | 5.53019i | 0.613072 | + | 0.790027i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 0.500983i | 0.280056 | − | 0.0701517i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.5830 | 1.72841 | 0.864204 | − | 0.503141i | \(-0.167822\pi\) | ||||
0.864204 | + | 0.503141i | \(0.167822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.06871 | + | 5.53019i | 0.413785 | + | 0.745691i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.64575 | + | 1.91520i | −1.01270 | + | 0.253674i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.91044 | −0.509095 | −0.254548 | − | 0.967060i | \(-0.581927\pi\) | ||||
−0.254548 | + | 0.967060i | \(0.581927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0808i | 1.29072i | 0.763878 | + | 0.645360i | \(0.223293\pi\) | ||||
−0.763878 | + | 0.645360i | \(0.776707\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.93227 | − | 0.281364i | 0.999372 | − | 0.0354486i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.64575 | − | 0.913230i | 0.204130 | − | 0.113272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.65489i | − | 0.568685i | −0.958723 | − | 0.284343i | \(-0.908225\pi\) | ||
0.958723 | − | 0.284343i | \(-0.0917753\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.38527 | + | 5.53019i | 0.166766 | + | 0.665757i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.6392i | − | 1.50000i | −0.661440 | − | 0.749998i | \(-0.730055\pi\) | ||
0.661440 | − | 0.749998i | \(-0.269945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.06871 | −0.359166 | −0.179583 | − | 0.983743i | \(-0.557475\pi\) | ||||
−0.179583 | + | 0.983743i | \(0.557475\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.24173 | + | 2.65967i | 0.951673 | + | 0.307113i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.29150 | − | 6.72057i | 0.375102 | − | 0.765880i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.29150 | 0.820358 | 0.410179 | − | 0.912005i | \(-0.365466\pi\) | ||||
0.410179 | + | 0.912005i | \(0.365466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | − | 7.48331i | 0.555556 | − | 0.831479i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.70010i | 0.845196i | 0.906317 | + | 0.422598i | \(0.138882\pi\) | ||||
−0.906317 | + | 0.422598i | \(0.861118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29150 | − | 2.32744i | −0.140083 | − | 0.252447i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.4148 | + | 3.36028i | −1.43821 | + | 0.360260i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8712 | 1.36435 | 0.682173 | − | 0.731191i | \(-0.261035\pi\) | ||||
0.682173 | + | 0.731191i | \(0.261035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | − | 0.979531i | −0.209657 | − | 0.102683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.29150 | + | 2.32744i | −0.963484 | + | 0.241345i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.93725 | + | 8.89753i | 0.506552 | + | 0.912867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.11905 | −0.824365 | −0.412182 | − | 0.911101i | \(-0.635233\pi\) | ||||
−0.412182 | + | 0.911101i | \(0.635233\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | − | 7.48331i | −0.402015 | − | 0.752101i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.91044 | −0.389103 | −0.194551 | − | 0.980892i | \(-0.562325\pi\) | ||||
−0.194551 | + | 0.980892i | \(0.562325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5730 | −1.23886 | −0.619429 | − | 0.785053i | \(-0.712636\pi\) | ||||
−0.619429 | + | 0.785053i | \(0.712636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.99501 | − | 9.79949i | −0.292283 | − | 0.956332i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.1669 | + | 4.55066i | −1.72433 | + | 0.431929i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.43560 | − | 3.57113i | 0.600123 | − | 0.333009i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.22699 | + | 1.19038i | −0.205885 | + | 0.110050i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.38527 | + | 2.82843i | −0.126987 | + | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.29150 | − | 13.1402i | −0.296785 | − | 1.18481i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.569951 | − | 11.1658i | 0.0509780 | − | 0.998700i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8127i | 0.959474i | 0.877412 | + | 0.479737i | \(0.159268\pi\) | ||||
−0.877412 | + | 0.479737i | \(0.840732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.82087 | + | 1.95906i | −0.688589 | + | 0.172486i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.96077 | 0.782906 | 0.391453 | − | 0.920198i | \(-0.371973\pi\) | ||||
0.391453 | + | 0.920198i | \(0.371973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29570 | − | 10.8127i | 0.459196 | − | 0.937582i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.0000 | − | 3.74166i | −0.946729 | − | 0.322031i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.29150 | −0.793827 | −0.396913 | − | 0.917856i | \(-0.629919\pi\) | ||||
−0.396913 | + | 0.917856i | \(0.629919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.6110i | − | 1.32411i | −0.749455 | − | 0.662056i | \(-0.769684\pi\) | ||
0.749455 | − | 0.662056i | \(-0.230316\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.29150 | − | 1.82646i | 0.614055 | − | 0.153816i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.38075i | 0.199088i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.66259 | + | 15.6110i | 0.719389 | + | 1.29643i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.48537 | + | 9.53778i | −0.617383 | + | 0.786662i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.32941i | 0.272756i | 0.990657 | + | 0.136378i | \(0.0435462\pi\) | ||||
−0.990657 | + | 0.136378i | \(0.956454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5830 | 1.83778 | 0.918889 | − | 0.394515i | \(-0.129087\pi\) | ||||
0.918889 | + | 0.394515i | \(0.129087\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.68345 | + | 3.14944i | 0.136099 | + | 0.254617i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | + | 10.8127i | 0.481932 | + | 0.868499i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.6209 | −1.80534 | −0.902672 | − | 0.430330i | \(-0.858397\pi\) | ||||
−0.902672 | + | 0.430330i | \(0.858397\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.29570 | + | 21.1412i | 0.419976 | + | 1.67661i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.82087 | − | 3.83039i | −0.616371 | − | 0.301877i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | + | 7.48331i | −0.622799 | + | 0.582575i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.4821i | − | 0.888509i | −0.895901 | − | 0.444255i | \(-0.853469\pi\) | ||
0.895901 | − | 0.444255i | \(-0.146531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2915 | −0.945500 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.43560 | − | 12.0399i | −0.492143 | − | 0.920715i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.89047i | 0.675930i | 0.941159 | + | 0.337965i | \(0.109739\pi\) | ||||
−0.941159 | + | 0.337965i | \(0.890261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2238 | + | 7.00193i | −0.848437 | + | 0.529296i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.64575 | − | 6.57008i | −0.123702 | − | 0.493838i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 9.48725i | − | 0.709110i | −0.935035 | − | 0.354555i | \(-0.884632\pi\) | ||
0.935035 | − | 0.354555i | \(-0.115368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.0399i | − | 0.894920i | −0.894304 | − | 0.447460i | \(-0.852329\pi\) | ||
0.894304 | − | 0.447460i | \(-0.147671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.9373 | + | 4.24264i | −1.25204 | + | 0.313625i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.7313 | + | 21.1412i | 0.862503 | + | 1.55433i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.36689 | 0.246211 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.81112 | + | 13.2089i | 0.277218 | + | 0.960807i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.98430i | − | 0.577724i | −0.957371 | − | 0.288862i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288862i | \(-0.0932768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528i | 0.610784i | 0.952227 | + | 0.305392i | \(0.0987875\pi\) | ||||
−0.952227 | + | 0.305392i | \(0.901213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.22699 | + | 2.38075i | 0.159478 | + | 0.170489i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5906i | 1.17607i | 0.808834 | + | 0.588037i | \(0.200099\pi\) | ||||
−0.808834 | + | 0.588037i | \(0.799901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.82087 | − | 1.95906i | 0.551642 | − | 0.138182i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.29150 | − | 18.9713i | 0.652136 | − | 1.33153i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.2915 | + | 8.48528i | −1.06800 | + | 0.592638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.70850 | + | 4.65489i | −0.605282 | + | 0.323537i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.8712 | −0.890320 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1660 | −1.45713 | −0.728564 | − | 0.684978i | \(-0.759812\pi\) | ||||
−0.728564 | + | 0.684978i | \(0.759812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.2356 | − | 5.31935i | 1.45504 | − | 0.364476i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.05034 | + | 9.10132i | 0.344430 | + | 0.620705i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.43560 | − | 13.1402i | 0.436877 | − | 0.892013i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.29150 | − | 5.15587i | −0.0872717 | − | 0.348401i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.00197i | − | 0.0673996i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.75216 | −0.318228 | −0.159114 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159114 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | + | 14.9666i | −0.0666667 | + | 0.997775i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.40122i | − | 0.0930023i | −0.998918 | − | 0.0465011i | \(-0.985193\pi\) | ||
0.998918 | − | 0.0465011i | \(-0.0148071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 28.2835i | − | 1.86903i | −0.355930 | − | 0.934513i | \(-0.615836\pi\) | ||
0.355930 | − | 0.934513i | \(-0.384164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.6768 | + | 2.70176i | 0.834070 | + | 0.177763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.70850 | 0.177440 | 0.0887198 | − | 0.996057i | \(-0.471722\pi\) | ||||
0.0887198 | + | 0.996057i | \(0.471722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.70850 | − | 8.48528i | −0.307149 | − | 0.553519i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.06871 | + | 12.2508i | 0.199334 | + | 0.795772i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1264i | 1.43124i | 0.698490 | + | 0.715620i | \(0.253856\pi\) | ||||
−0.698490 | + | 0.715620i | \(0.746144\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.95906i | − | 0.126194i | −0.998007 | − | 0.0630972i | \(-0.979902\pi\) | ||
0.998007 | − | 0.0630972i | \(-0.0200978\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6773 | + | 5.25127i | 0.941551 | + | 0.336869i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.3908 | + | 6.15664i | 0.919396 | + | 0.393334i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.83039i | 0.243722i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.9373 | + | 3.24067i | −0.819865 | + | 0.205369i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7313 | 0.740473 | 0.370237 | − | 0.928937i | \(-0.379277\pi\) | ||||
0.370237 | + | 0.928937i | \(0.379277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.30978i | 0.585301i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.36689 | − | 3.14944i | 0.210843 | − | 0.197225i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 14.2098i | − | 0.886384i | −0.896427 | − | 0.443192i | \(-0.853846\pi\) | ||
0.896427 | − | 0.443192i | \(-0.146154\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5830 | − | 25.6919i | 0.781870 | − | 1.59642i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.2915 | − | 21.1245i | −0.698926 | − | 1.30757i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.58301 | 0.405925 | 0.202963 | − | 0.979186i | \(-0.434943\pi\) | ||||
0.202963 | + | 0.979186i | \(0.434943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.6025 | − | 13.6520i | 1.51132 | − | 0.838634i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.41699 | + | 21.6255i | 0.331515 | + | 1.32346i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.6025 | 1.50004 | 0.750021 | − | 0.661414i | \(-0.230043\pi\) | ||||
0.750021 | + | 0.661414i | \(0.230043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.48925i | − | 0.454940i | −0.973785 | − | 0.227470i | \(-0.926955\pi\) | ||
0.973785 | − | 0.227470i | \(-0.0730453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.804028 | − | 3.77253i | 0.0486620 | − | 0.228324i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | + | 7.48331i | 0.723627 | + | 0.451261i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 15.4676i | − | 0.929359i | −0.885479 | − | 0.464679i | \(-0.846170\pi\) | ||
0.885479 | − | 0.464679i | \(-0.153830\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.82087 | − | 14.6315i | −0.468223 | − | 0.875965i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.6235i | − | 1.23029i | −0.788412 | − | 0.615147i | \(-0.789097\pi\) | ||
0.788412 | − | 0.615147i | \(-0.210903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.74968 | 0.579558 | 0.289779 | − | 0.957094i | \(-0.406418\pi\) | ||||
0.289779 | + | 0.957094i | \(0.406418\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.8712 | + | 12.0399i | −0.762425 | + | 0.713183i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.5830 | + | 9.10132i | 1.09692 | + | 0.537234i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5830 | 0.916647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.41699 | − | 13.6412i | −0.200308 | − | 0.799659i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 11.2712i | − | 0.658472i | −0.944248 | − | 0.329236i | \(-0.893209\pi\) | ||
0.944248 | − | 0.329236i | \(-0.106791\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.64575 | + | 4.24264i | −0.445153 | + | 0.247016i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.8896 | − | 9.87000i | 0.631878 | − | 0.572716i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.77053 | 0.160224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.41699 | − | 11.0604i | 0.312230 | − | 0.637510i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.64575 | − | 6.57008i | −0.0945459 | − | 0.377441i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9373 | + | 19.7103i | 0.626265 | + | 1.12861i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8000 | 0.844682 | 0.422341 | − | 0.906437i | \(-0.361209\pi\) | ||||
0.422341 | + | 0.906437i | \(0.361209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.29150 | − | 21.1245i | −0.301023 | − | 1.20173i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.77053 | −0.157103 | −0.0785513 | − | 0.996910i | \(-0.525029\pi\) | ||||
−0.0785513 | + | 0.996910i | \(0.525029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.11905 | −0.458916 | −0.229458 | − | 0.973319i | \(-0.573695\pi\) | ||||
−0.229458 | + | 0.973319i | \(0.573695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.2040 | − | 9.15627i | 0.856650 | − | 0.515897i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5830 | −1.26441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.41699 | 0.301410 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22699 | − | 3.57113i | 0.123531 | − | 0.198091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.841723 | + | 3.36028i | 0.0465474 | + | 0.185824i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.05034 | + | 10.3117i | −0.278434 | + | 0.568505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.2915 | − | 28.6078i | −0.837969 | − | 1.56770i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.05034 | − | 9.10132i | −0.275929 | − | 0.497258i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.4499i | 1.22293i | 0.791273 | + | 0.611463i | \(0.209419\pi\) | ||||
−0.791273 | + | 0.611463i | \(0.790581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.52517 | − | 10.0808i | −0.137148 | − | 0.547517i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.6417 | −0.847048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.76135 | − | 18.1343i | −0.203094 | − | 0.979159i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.70850 | + | 9.30978i | 0.468850 | + | 0.501221i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000 | 1.28839 | 0.644194 | − | 0.764862i | \(-0.277193\pi\) | ||||
0.644194 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1822i | 1.02680i | 0.858150 | + | 0.513399i | \(0.171614\pi\) | ||||
−0.858150 | + | 0.513399i | \(0.828386\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.93725 | − | 3.24067i | −0.156779 | − | 0.172974i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 21.3521i | − | 1.13646i | −0.822871 | − | 0.568228i | \(-0.807629\pi\) | ||
0.822871 | − | 0.568228i | \(-0.192371\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7129 | − | 24.7124i | −0.727807 | − | 1.31160i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.33516 | − | 1.13707i | −0.282367 | − | 0.0601800i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.7813i | 1.41346i | 0.707481 | + | 0.706732i | \(0.249831\pi\) | ||||
−0.707481 | + | 0.706732i | \(0.750169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.70850 | −0.0899209 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.26258 | + | 5.04042i | 0.0662685 | + | 0.264554i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | + | 3.32941i | −0.314054 | + | 0.174269i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.11905 | 0.423811 | 0.211905 | − | 0.977290i | \(-0.432033\pi\) | ||||
0.211905 | + | 0.977290i | \(0.432033\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.6921 | − | 11.0604i | 1.07719 | − | 0.575780i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.8982 | − | 14.6431i | −1.55224 | − | 0.760233i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4676i | 0.800883i | 0.916322 | + | 0.400441i | \(0.131143\pi\) | ||||
−0.916322 | + | 0.400441i | \(0.868857\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0000 | − | 3.74166i | 0.981156 | − | 0.193218i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.72057i | 0.346127i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5830 | −0.749079 | −0.374539 | − | 0.927211i | \(-0.622199\pi\) | ||||
−0.374539 | + | 0.927211i | \(0.622199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1669 | + | 4.55066i | −0.930719 | + | 0.233137i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11.4821i | − | 0.586706i | −0.956004 | − | 0.293353i | \(-0.905229\pi\) | ||
0.956004 | − | 0.293353i | \(-0.0947712\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.855899 | − | 16.7113i | −0.0436206 | − | 0.851687i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.58301 | − | 12.3157i | −0.334633 | − | 0.626041i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.323511i | 0.0164026i | 0.999966 | + | 0.00820132i | \(0.00261059\pi\) | ||||
−0.999966 | + | 0.00820132i | \(0.997389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.91813i | − | 0.198148i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.77124 | + | 15.0554i | 0.190234 | + | 0.759443i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.2565 | − | 7.91094i | 0.717321 | − | 0.398043i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5338 | 1.08075 | 0.540375 | − | 0.841424i | \(-0.318282\pi\) | ||||
0.540375 | + | 0.841424i | \(0.318282\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.3957 | + | 4.34687i | 1.02106 | + | 0.217616i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.48331i | − | 0.373699i | −0.982389 | − | 0.186849i | \(-0.940172\pi\) | ||
0.982389 | − | 0.186849i | \(-0.0598277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.65489i | 0.231876i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.65704 | − | 20.0563i | 0.0823389 | − | 0.996604i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.5830 | −1.51594 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.0194i | − | 0.643770i | −0.946779 | − | 0.321885i | \(-0.895684\pi\) | ||
0.946779 | − | 0.321885i | \(-0.104316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.91044 | − | 15.6110i | −0.192888 | − | 0.770036i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.29150 | + | 4.55066i | 0.457205 | + | 0.223923i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.35425 | + | 15.0554i | 0.410094 | + | 0.739039i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.2288 | − | 6.57008i | 1.28443 | − | 0.321738i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.8320 | 1.06656 | 0.533281 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533281 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.13742 | + | 11.4821i | 0.298412 | + | 0.558277i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.05034 | − | 3.14944i | −0.244977 | − | 0.152770i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.7313 | − | 23.9529i | 0.567718 | − | 1.15916i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | + | 1.00197i | −0.193122 | + | 0.0483754i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.4696i | − | 0.793312i | −0.917967 | − | 0.396656i | \(-0.870171\pi\) | ||
0.917967 | − | 0.396656i | \(-0.129829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.5313 | −1.27501 | −0.637507 | − | 0.770445i | \(-0.720034\pi\) | ||||
−0.637507 | + | 0.770445i | \(0.720034\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.5830 | + | 21.1245i | −1.08277 | + | 1.01284i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.9785i | 0.716519i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5496i | 0.885326i | 0.896688 | + | 0.442663i | \(0.145966\pi\) | ||||
−0.896688 | + | 0.442663i | \(0.854034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1751 | − | 8.56241i | −0.913101 | − | 0.407734i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1660 | −0.625536 | −0.312768 | − | 0.949830i | \(-0.601256\pi\) | ||||
−0.312768 | + | 0.949830i | \(0.601256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.1660 | − | 13.9647i | 1.19298 | − | 0.661989i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.59388 | + | 1.40122i | −0.264581 | + | 0.0662755i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.30781i | − | 0.392070i | −0.980597 | − | 0.196035i | \(-0.937193\pi\) | ||
0.980597 | − | 0.196035i | \(-0.0628066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.1208i | − | 1.04163i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.50432 | + | 37.9426i | 0.446552 | + | 1.78270i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.97318 | + | 0.254710i | −0.233146 | + | 0.0119410i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.48528i | − | 0.396925i | −0.980109 | − | 0.198462i | \(-0.936405\pi\) | ||
0.980109 | − | 0.198462i | \(-0.0635948\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.58301 | + | 4.15390i | −0.213916 | + | 0.193888i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.96077 | 0.417345 | 0.208672 | − | 0.977986i | \(-0.433086\pi\) | ||||
0.208672 | + | 0.977986i | \(0.433086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.9529i | 1.11319i | 0.830786 | + | 0.556593i | \(0.187892\pi\) | ||||
−0.830786 | + | 0.556593i | \(0.812108\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.6417 | + | 14.6315i | −0.725368 | + | 0.678520i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3.36028i | − | 0.155495i | −0.996973 | − | 0.0777477i | \(-0.975227\pi\) | ||
0.996973 | − | 0.0777477i | \(-0.0247729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.41699 | + | 11.0604i | −0.250134 | + | 0.510721i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.52026 | − | 38.0063i | −0.438670 | − | 1.75124i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1660 | −0.605374 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.3068 | + | 12.0399i | 0.885857 | + | 0.552429i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −33.2915 | + | 17.7951i | −1.52431 | + | 0.814780i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.1044 | 1.78672 | 0.893362 | − | 0.449338i | \(-0.148340\pi\) | ||||
0.893362 | + | 0.449338i | \(0.148340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.10132i | 0.414984i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.14410 | − | 14.7522i | 0.143062 | − | 0.671250i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8745 | + | 8.80879i | −0.720824 | + | 0.399987i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.4382i | − | 1.46991i | −0.678114 | − | 0.734957i | \(-0.737202\pi\) | ||
0.678114 | − | 0.734957i | \(-0.262798\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14.1421i | − | 0.638226i | −0.947717 | − | 0.319113i | \(-0.896615\pi\) | ||
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.50432 | 0.428053 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.9399 | − | 10.2917i | −0.716446 | − | 0.462577i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.7085 | + | 30.0317i | −0.659766 | + | 1.34711i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.41699 | −0.0634334 | −0.0317167 | − | 0.999497i | \(-0.510097\pi\) | ||||
−0.0317167 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.2915 | − | 4.83236i | 0.861881 | − | 0.215894i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.67963i | 0.387006i | 0.981100 | + | 0.193503i | \(0.0619848\pi\) | ||||
−0.981100 | + | 0.193503i | \(0.938015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.64575 | + | 4.24264i | −0.340231 | + | 0.188795i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.17302 | − | 20.6515i | −0.229742 | − | 0.917164i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.1436 | −1.33609 | −0.668045 | − | 0.744121i | \(-0.732869\pi\) | ||||
−0.668045 | + | 0.744121i | \(0.732869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.29150 | + | 3.57113i | 0.322557 | + | 0.157977i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5203 | − | 15.8799i | 0.773538 | − | 0.701113i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.5830 | + | 13.6412i | −1.08326 | + | 0.601101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2748 | 0.539847 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9373 | + | 3.74166i | −0.655673 | + | 0.164241i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4626 | 1.02792 | 0.513958 | − | 0.857815i | \(-0.328179\pi\) | ||||
0.513958 | + | 0.857815i | \(0.328179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.20861 | 0.184030 | 0.0920149 | − | 0.995758i | \(-0.470669\pi\) | ||||
0.0920149 | + | 0.995758i | \(0.470669\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.4879 | − | 15.9107i | −0.719590 | − | 0.694399i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.58301 | 0.286760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.1660 | −0.528957 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3460 | − | 5.53019i | 0.448980 | − | 0.239990i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.58301 | −0.285142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.9399 | − | 3.99282i | 0.687858 | − | 0.172303i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.6417 | + | 12.1382i | −0.673737 | + | 0.522829i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2288 | − | 5.06713i | 0.868099 | − | 0.217452i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.91044 | − | 2.16991i | 0.167505 | − | 0.0929486i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.9706i | − | 0.725609i | −0.931865 | − | 0.362804i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362804i | \(-0.118181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.2565 | − | 26.6714i | −0.608451 | − | 1.13831i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.3338 | −1.54787 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3252 | − | 8.48528i | −0.736742 | − | 0.360831i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.5830 | + | 28.6078i | −1.29818 | + | 1.21433i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.16601 | 0.303634 | 0.151817 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151817 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.91813i | 0.165719i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41699 | + | 5.65685i | 0.0598256 | + | 0.238833i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.7605i | 0.790660i | 0.918539 | + | 0.395330i | \(0.129370\pi\) | ||||
−0.918539 | + | 0.395330i | \(0.870630\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.7313 | + | 6.50972i | −0.493540 | + | 0.273866i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.5889 | + | 11.9623i | −0.864652 | + | 0.502371i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.1362i | 0.466855i | 0.972374 | + | 0.233428i | \(0.0749942\pi\) | ||||
−0.972374 | + | 0.233428i | \(0.925006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5830 | 1.44725 | 0.723627 | − | 0.690191i | \(-0.242474\pi\) | ||||
0.723627 | + | 0.690191i | \(0.242474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4148 | − | 3.36028i | 0.560409 | − | 0.140378i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.70850 | − | 13.9647i | 0.363169 | − | 0.582367i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.9853 | 1.28993 | 0.644967 | − | 0.764210i | \(-0.276871\pi\) | ||||
0.644967 | + | 0.764210i | \(0.276871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.2565 | + | 3.57113i | −0.592479 | + | 0.148411i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.96077 | − | 18.2960i | 0.371755 | − | 0.759048i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.5901i | 1.47399i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.06275 | + | 4.74362i | −0.126629 | + | 0.196125i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.1054i | 1.82042i | 0.414143 | + | 0.910212i | \(0.364081\pi\) | ||||
−0.414143 | + | 0.910212i | \(0.635919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.1660 | −1.03695 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.57551 | + | 30.2425i | 0.311615 | + | 1.24401i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.91094i | 0.324863i | 0.986720 | + | 0.162432i | \(0.0519337\pi\) | ||||
−0.986720 | + | 0.162432i | \(0.948066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.360215 | + | 7.03314i | 0.0147674 | + | 0.288331i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.8745 | + | 6.98233i | −1.14083 | + | 0.285768i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2960i | 0.747556i | 0.927518 | + | 0.373778i | \(0.121938\pi\) | ||||
−0.927518 | + | 0.373778i | \(0.878062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.0604i | − | 0.451162i | −0.974224 | − | 0.225581i | \(-0.927572\pi\) | ||
0.974224 | − | 0.225581i | \(-0.0724281\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.58301 | + | 12.3157i | 0.268081 | + | 0.501533i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.86565 | − | 3.25486i | 0.238473 | − | 0.132329i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7608 | 0.964421 | 0.482210 | − | 0.876055i | \(-0.339834\pi\) | ||||
0.482210 | + | 0.876055i | \(0.339834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.7849 | + | 7.62674i | 1.45008 | + | 0.309051i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.65292i | − | 0.147781i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 40.0990i | − | 1.61958i | −0.586719 | − | 0.809791i | \(-0.699581\pi\) | ||
0.586719 | − | 0.809791i | \(-0.300419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.6921 | − | 22.1208i | −0.834385 | − | 0.891995i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.83399 | 0.194609 | 0.0973045 | − | 0.995255i | \(-0.468978\pi\) | ||||
0.0973045 | + | 0.995255i | \(0.468978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.632534i | 0.0254237i | 0.999919 | + | 0.0127118i | \(0.00404641\pi\) | ||||
−0.999919 | + | 0.0127118i | \(0.995954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4859 | − | 12.6724i | −0.460915 | − | 0.508528i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.5830 | − | 14.9785i | −1.22528 | − | 0.600101i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | − | 22.4499i | −0.440000 | − | 0.897998i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.41699 | − | 21.6255i | −0.216334 | − | 0.863637i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.8712 | 0.513209 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4575 | 0.814401 | 0.407200 | − | 0.913339i | \(-0.366505\pi\) | ||||
0.407200 | + | 0.913339i | \(0.366505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.90796 | − | 35.5619i | −0.354060 | − | 1.41346i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.7313 | + | 21.1412i | 0.465543 | + | 0.838964i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61226 | + | 4.65489i | 0.143123 | + | 0.184433i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.8745 | + | 33.4401i | 0.707105 | + | 1.32287i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 16.7931i | − | 0.663287i | −0.943405 | − | 0.331644i | \(-0.892397\pi\) | ||
0.943405 | − | 0.331644i | \(-0.107603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −47.7669 | −1.88374 | −0.941872 | − | 0.335971i | \(-0.890935\pi\) | ||||
−0.941872 | + | 0.335971i | \(0.890935\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.1660 | + | 12.3157i | −0.518411 | + | 0.484929i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.4002i | − | 0.605444i | −0.953079 | − | 0.302722i | \(-0.902105\pi\) | ||
0.953079 | − | 0.302722i | \(-0.0978954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.0604i | − | 0.434158i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.7858 | + | 5.28253i | 0.971434 | + | 0.207039i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.1660 | 0.750024 | 0.375012 | − | 0.927020i | \(-0.377639\pi\) | ||||
0.375012 | + | 0.927020i | \(0.377639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.5203 | − | 9.72202i | 0.684573 | − | 0.379871i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.11905 | − | 4.33981i | 0.316754 | − | 0.169312i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.7617i | − | 1.27621i | −0.769948 | − | 0.638107i | \(-0.779718\pi\) | ||
0.769948 | − | 0.638107i | \(-0.220282\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.979531i | − | 0.0380994i | −0.999819 | − | 0.0190497i | \(-0.993936\pi\) | ||
0.999819 | − | 0.0190497i | \(-0.00606407\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.68345 | − | 0.421689i | 0.0653796 | − | 0.0163770i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.37706 | − | 26.8868i | −0.0534000 | − | 1.04263i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.2803i | 1.01758i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 7.98430i | −0.0773245 | − | 0.308691i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.5129 | −1.10073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.5960i | 1.48777i | 0.668309 | + | 0.743883i | \(0.267018\pi\) | ||||
−0.668309 | + | 0.743883i | \(0.732982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.5669 | + | 4.61874i | −0.984071 | + | 0.177775i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 42.4933i | − | 1.63315i | −0.577239 | − | 0.816575i | \(-0.695870\pi\) | ||
0.577239 | − | 0.816575i | \(-0.304130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.2915 | + | 9.44832i | 0.740340 | + | 0.362593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.35425 | − | 0.589720i | 0.0902150 | − | 0.0225981i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.41699 | −0.207276 | −0.103638 | − | 0.994615i | \(-0.533048\pi\) | ||||
−0.103638 | + | 0.994615i | \(0.533048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.1669 | + | 10.0808i | −0.694122 | + | 0.385169i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.5203 | − | 11.9034i | 1.81301 | − | 0.454144i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5914 | 0.403500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.50972i | 0.247641i | 0.992305 | + | 0.123821i | \(0.0395148\pi\) | ||||
−0.992305 | + | 0.123821i | \(0.960485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.795819 | + | 22.4358i | 0.0302306 | + | 0.852267i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.9373 | − | 30.5230i | −0.642467 | − | 1.15780i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.30978i | 0.352633i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.13990 | + | 4.55066i | 0.0431151 | + | 0.172122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.32548i | − | 0.0500626i | −0.999687 | − | 0.0250313i | \(-0.992031\pi\) | ||
0.999687 | − | 0.0250313i | \(-0.00796854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.2050 | −1.85580 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.2748 | − | 11.4821i | 0.462298 | − | 0.432440i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.29150 | + | 4.55066i | 0.349443 | + | 0.171145i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5830 | 0.773011 | 0.386505 | − | 0.922287i | \(-0.373682\pi\) | ||||
0.386505 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.2915 | + | 10.3117i | −0.723488 | + | 0.386721i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.2026i | 0.681694i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.58301 | + | 4.65489i | 0.0965989 | + | 0.174083i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.1755 | + | 9.31216i | −1.38835 | + | 0.347769i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.3338 | −1.35502 | −0.677511 | − | 0.735512i | \(-0.736942\pi\) | ||||
−0.677511 | + | 0.735512i | \(0.736942\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.8745 | + | 14.6315i | 1.11258 | + | 0.544906i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.29150 | − | 0.824494i | 0.122412 | − | 0.0306633i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.8745 | + | 21.1245i | 1.25807 | + | 0.784543i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.03196 | −0.260801 | −0.130401 | − | 0.991461i | \(-0.541626\pi\) | ||||
−0.130401 | + | 0.991461i | \(0.541626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.64575 | + | 26.8701i | −0.0979908 | + | 0.995187i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.54107 | 0.204944 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.9007 | −0.919728 | −0.459864 | − | 0.887989i | \(-0.652102\pi\) | ||||
−0.459864 | + | 0.887989i | \(0.652102\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.28749 | + | 26.7697i | −0.158147 | + | 0.987416i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.1660 | 0.484976 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.16601 | −0.337177 | −0.168589 | − | 0.985687i | \(-0.553921\pi\) | ||||
−0.168589 | + | 0.985687i | \(0.553921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.43560 | + | 1.61206i | −0.236418 | + | 0.0592207i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.8745 | 1.24274 | 0.621368 | − | 0.783519i | \(-0.286577\pi\) | ||||
0.621368 | + | 0.783519i | \(0.286577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.61226 | + | 6.50972i | 0.132343 | + | 0.238498i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8896 | − | 20.3725i | −0.398429 | − | 0.745392i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.1660 | −0.772359 | −0.386179 | − | 0.922424i | \(-0.626205\pi\) | ||||
−0.386179 | + | 0.922424i | \(0.626205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.93725 | + | 19.7103i | 0.179924 | + | 0.718282i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44.1547 | − | 24.5015i | 1.60695 | − | 0.891701i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.15194i | − | 0.114559i | −0.998358 | − | 0.0572796i | \(-0.981757\pi\) | ||
0.998358 | − | 0.0572796i | \(-0.0182426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.6417 | + | 3.91813i | −0.567759 | + | 0.142219i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6921 | −0.750087 | −0.375044 | − | 0.927007i | \(-0.622372\pi\) | ||||
−0.375044 | + | 0.927007i | \(0.622372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.75216 | − | 2.32744i | −0.172040 | − | 0.0842591i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.70850 | + | 4.33138i | 0.242546 | + | 0.156601i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.29150 | −0.118849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.1402i | 1.26719i | 0.773666 | + | 0.633594i | \(0.218421\pi\) | ||||
−0.773666 | + | 0.633594i | \(0.781579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.8745 | − | 5.98036i | 0.859819 | − | 0.215378i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 7.35310i | − | 0.264473i | −0.991218 | − | 0.132236i | \(-0.957784\pi\) | ||
0.991218 | − | 0.132236i | \(-0.0422158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.4626 | + | 14.6315i | 0.842802 | + | 0.525579i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 48.4617 | + | 10.3285i | 1.73855 | + | 0.370533i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 35.5901i | − | 1.27515i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.7490 | 1.27920 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.7399 | − | 27.8618i | 1.09856 | − | 0.995699i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.2288 | + | 24.5426i | −1.57859 | + | 0.875963i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.9007 | 0.887614 | 0.443807 | − | 0.896122i | \(-0.353628\pi\) | ||||
0.443807 | + | 0.896122i | \(0.353628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.77053 | + | 11.0604i | 0.0986336 | + | 0.393760i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2565 | + | 6.98233i | 0.506902 | + | 0.248263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.48528i | 0.301321i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.2915 | + | 35.5901i | 1.18073 | + | 1.26225i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.93141i | 0.245523i | 0.992436 | + | 0.122762i | \(0.0391750\pi\) | ||||
−0.992436 | + | 0.122762i | \(0.960825\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.16601 | −0.182760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.0540 | + | 18.2026i | −1.20324 | + | 0.643159i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.67963i | − | 0.306297i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.4473 | + | 0.996028i | −0.685427 | + | 0.0351054i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.3542 | + | 41.3357i | 0.364487 | + | 1.45509i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 33.7637i | − | 1.18707i | −0.804809 | − | 0.593533i | \(-0.797732\pi\) | ||
0.804809 | − | 0.593533i | \(-0.202268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.6305i | 1.00535i | 0.864475 | + | 0.502676i | \(0.167651\pi\) | ||||
−0.864475 | + | 0.502676i | \(0.832349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5830 | − | 3.15194i | 0.441305 | − | 0.110543i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.1828 | −0.741093 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.67677 | − | 0.236831i | 0.233305 | − | 0.00827554i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.98036i | − | 0.208716i | −0.994540 | − | 0.104358i | \(-0.966721\pi\) | ||
0.994540 | − | 0.104358i | \(-0.0332788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.2980i | − | 0.672686i | −0.941740 | − | 0.336343i | \(-0.890810\pi\) | ||
0.941740 | − | 0.336343i | \(-0.109190\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.52269 | + | 23.3111i | −0.261906 | + | 0.811590i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.2211i | 1.57059i | 0.619120 | + | 0.785296i | \(0.287489\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.9878 | − | 6.50972i | 0.901506 | − | 0.225820i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.58301 | − | 5.10850i | 0.228088 | − | 0.176999i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4575 | − | 22.4499i | −0.431110 | − | 0.776912i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.2915 | − | 19.2980i | 0.735942 | − | 0.667037i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.2331 | 0.905669 | 0.452834 | − | 0.891595i | \(-0.350413\pi\) | ||||
0.452834 | + | 0.891595i | \(0.350413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.7490 | −1.19824 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.6504 | − | 8.67963i | 1.19342 | − | 0.298942i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.0326 | + | 13.3357i | −0.826745 | + | 0.458762i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.12824 | − | 3.49117i | −0.244929 | − | 0.119958i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.10326 | + | 16.3808i | 0.140824 | + | 0.562189i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5901i | 1.22001i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.89206 | 0.201740 | 0.100870 | − | 0.994900i | \(-0.467837\pi\) | ||||
0.100870 | + | 0.994900i | \(0.467837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.6458 | − | 16.5583i | −0.877066 | − | 0.566282i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1545i | 0.825103i | 0.910934 | + | 0.412551i | \(0.135362\pi\) | ||||
−0.910934 | + | 0.412551i | \(0.864638\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.59160i | 0.0884241i | 0.999022 | + | 0.0442121i | \(0.0140777\pi\) | ||||
−0.999022 | + | 0.0442121i | \(0.985922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.47063 | + | 35.0525i | −0.254598 | + | 1.19459i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.64575 | + | 17.3828i | 0.327965 | + | 0.591033i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.55829 | + | 26.1817i | 0.222731 | + | 0.889176i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.6235i | 0.699604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.91813i | − | 0.132761i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.4810 | − | 11.4821i | 0.727021 | − | 0.388609i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.3481 | + | 25.8676i | −0.485056 | + | 0.874483i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.50295i | 0.0507510i | 0.999678 | + | 0.0253755i | \(0.00807814\pi\) | ||||
−0.999678 | + | 0.0253755i | \(0.991922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.9373 | − | 4.74362i | 0.638738 | − | 0.159998i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.8712 | −0.433642 | −0.216821 | − | 0.976211i | \(-0.569569\pi\) | ||||
−0.216821 | + | 0.976211i | \(0.569569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.9647i | 0.469948i | 0.972002 | + | 0.234974i | \(0.0755006\pi\) | ||||
−0.972002 | + | 0.234974i | \(0.924499\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.3460 | − | 11.0604i | −0.347778 | − | 0.371791i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 44.6632i | − | 1.49964i | −0.661640 | − | 0.749822i | \(-0.730139\pi\) | ||
0.661640 | − | 0.749822i | \(-0.269861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.5830 | − | 25.6919i | 0.422020 | − | 0.861678i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.1660 | + | 14.1421i | 0.709088 | + | 0.473779i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.7490 | 0.660876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.2932 | − | 18.5496i | −0.344065 | − | 0.620046i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.16601 | + | 4.65489i | 0.0389320 | + | 0.155422i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44.1547 | −1.47264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.9785i | − | 0.499006i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.8628 | + | 4.44643i | 0.694271 | + | 0.147968i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.0627 | − | 23.5406i | −0.434220 | − | 0.782518i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.9411i | 1.12700i | 0.826117 | + | 0.563498i | \(0.190545\pi\) | ||||
−0.826117 | + | 0.563498i | \(0.809455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3460 | − | 5.53019i | 0.343156 | − | 0.183425i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.15390i | − | 0.137625i | −0.997630 | − | 0.0688125i | \(-0.978079\pi\) | ||
0.997630 | − | 0.0688125i | \(-0.0219210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.7792 | −0.720785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.5129 | + | 26.6714i | −0.942609 | + | 0.881730i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.2915 | − | 10.4278i | −0.703107 | − | 0.344358i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.1255 | −0.334009 | −0.167005 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.22876 | + | 24.8661i | 0.205245 | + | 0.819367i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.6387i | − | 0.350177i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.8745 | + | 28.6078i | 1.50834 | + | 0.940618i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.2651 | − | 17.7809i | 1.09257 | − | 0.584003i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.7928 | −1.01028 | −0.505139 | − | 0.863038i | \(-0.668559\pi\) | ||||
−0.505139 | + | 0.863038i | \(0.668559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.1660 | + | 19.5292i | −0.824783 | + | 0.640043i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.16601 | − | 4.65489i | −0.0381735 | − | 0.152394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.58301 | − | 3.65292i | 0.215287 | − | 0.119463i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.06871 | −0.100250 | −0.0501252 | − | 0.998743i | \(-0.515962\pi\) | ||||
−0.0501252 | + | 0.998743i | \(0.515962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.41699 | − | 13.6412i | −0.111509 | − | 0.445162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.2443 | 1.31193 | 0.655963 | − | 0.754793i | \(-0.272263\pi\) | ||||
0.655963 | + | 0.754793i | \(0.272263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.7424 | −0.838288 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21.7826 | + | 21.6914i | 0.708589 | + | 0.705622i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0000 | −0.779895 | −0.389948 | − | 0.920837i | \(-0.627507\pi\) | ||||
−0.389948 | + | 0.920837i | \(0.627507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.58301 | −0.0838479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.52517 | + | 10.0808i | 0.0818842 | + | 0.326894i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.8745 | −0.902944 | −0.451472 | − | 0.892285i | \(-0.649101\pi\) | ||||
−0.451472 | + | 0.892285i | \(0.649101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.66259 | − | 15.6110i | −0.280315 | − | 0.505161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.50432 | − | 37.9426i | −0.307231 | − | 1.22651i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.0773 | + | 10.8127i | 0.712915 | + | 0.349161i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.416995 | 0.0134514 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.20614 | + | 16.5906i | 0.296356 | + | 0.534069i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4087i | 1.58888i | 0.607344 | + | 0.794439i | \(0.292235\pi\) | ||||
−0.607344 | + | 0.794439i | \(0.707765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.27980 | + | 9.10132i | 0.0732379 | + | 0.292376i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.6025 | −0.789532 | −0.394766 | − | 0.918782i | \(-0.629174\pi\) | ||||
−0.394766 | + | 0.918782i | \(0.629174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.1669 | + | 37.0931i | −0.582404 | + | 1.18915i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.93725 | + | 2.23871i | 0.222170 | + | 0.0716960i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.8745 | −1.65961 | −0.829806 | − | 0.558052i | \(-0.811549\pi\) | ||||
−0.829806 | + | 0.558052i | \(0.811549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.4053i | 1.16352i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.29150 | + | 2.82843i | −0.168945 | + | 0.0903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 62.0225i | 1.97821i | 0.147213 | + | 0.989105i | \(0.452970\pi\) | ||||
−0.147213 | + | 0.989105i | \(0.547030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.1939 | − | 19.5292i | 1.12137 | − | 0.622251i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.4507 | − | 4.14547i | −0.619122 | − | 0.131952i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.3216i | 0.487198i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.708497 | 0.0225062 | 0.0112531 | − | 0.999937i | \(-0.496418\pi\) | ||||
0.0112531 | + | 0.999937i | \(0.496418\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.36689 | − | 13.4411i | −0.106845 | − | 0.426541i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0000 | + | 32.4382i | 0.570638 | + | 1.02836i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.2259 | 1.33731 | 0.668653 | − | 0.743574i | \(-0.266871\pi\) | ||||
0.668653 | + | 0.743574i | \(0.266871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41.6295 | − | 37.7318i | 1.31710 | − | 1.19378i |
(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 | 1680.2.k.e.209.6 | 8 | ||
3.2 | odd | 2 | 1680.2.k.f.209.5 | 8 | |||
4.3 | odd | 2 | 210.2.d.a.209.3 | ✓ | 8 | ||
5.4 | even | 2 | 1680.2.k.f.209.3 | 8 | |||
7.6 | odd | 2 | inner | 1680.2.k.e.209.3 | 8 | ||
12.11 | even | 2 | 210.2.d.b.209.4 | yes | 8 | ||
15.14 | odd | 2 | inner | 1680.2.k.e.209.4 | 8 | ||
20.3 | even | 4 | 1050.2.b.f.251.15 | 16 | |||
20.7 | even | 4 | 1050.2.b.f.251.2 | 16 | |||
20.19 | odd | 2 | 210.2.d.b.209.6 | yes | 8 | ||
21.20 | even | 2 | 1680.2.k.f.209.4 | 8 | |||
28.27 | even | 2 | 210.2.d.a.209.6 | yes | 8 | ||
35.34 | odd | 2 | 1680.2.k.f.209.6 | 8 | |||
60.23 | odd | 4 | 1050.2.b.f.251.1 | 16 | |||
60.47 | odd | 4 | 1050.2.b.f.251.16 | 16 | |||
60.59 | even | 2 | 210.2.d.a.209.5 | yes | 8 | ||
84.83 | odd | 2 | 210.2.d.b.209.5 | yes | 8 | ||
105.104 | even | 2 | inner | 1680.2.k.e.209.5 | 8 | ||
140.27 | odd | 4 | 1050.2.b.f.251.7 | 16 | |||
140.83 | odd | 4 | 1050.2.b.f.251.10 | 16 | |||
140.139 | even | 2 | 210.2.d.b.209.3 | yes | 8 | ||
420.83 | even | 4 | 1050.2.b.f.251.8 | 16 | |||
420.167 | even | 4 | 1050.2.b.f.251.9 | 16 | |||
420.419 | odd | 2 | 210.2.d.a.209.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.d.a.209.3 | ✓ | 8 | 4.3 | odd | 2 | ||
210.2.d.a.209.4 | yes | 8 | 420.419 | odd | 2 | ||
210.2.d.a.209.5 | yes | 8 | 60.59 | even | 2 | ||
210.2.d.a.209.6 | yes | 8 | 28.27 | even | 2 | ||
210.2.d.b.209.3 | yes | 8 | 140.139 | even | 2 | ||
210.2.d.b.209.4 | yes | 8 | 12.11 | even | 2 | ||
210.2.d.b.209.5 | yes | 8 | 84.83 | odd | 2 | ||
210.2.d.b.209.6 | yes | 8 | 20.19 | odd | 2 | ||
1050.2.b.f.251.1 | 16 | 60.23 | odd | 4 | |||
1050.2.b.f.251.2 | 16 | 20.7 | even | 4 | |||
1050.2.b.f.251.7 | 16 | 140.27 | odd | 4 | |||
1050.2.b.f.251.8 | 16 | 420.83 | even | 4 | |||
1050.2.b.f.251.9 | 16 | 420.167 | even | 4 | |||
1050.2.b.f.251.10 | 16 | 140.83 | odd | 4 | |||
1050.2.b.f.251.15 | 16 | 20.3 | even | 4 | |||
1050.2.b.f.251.16 | 16 | 60.47 | odd | 4 | |||
1680.2.k.e.209.3 | 8 | 7.6 | odd | 2 | inner | ||
1680.2.k.e.209.4 | 8 | 15.14 | odd | 2 | inner | ||
1680.2.k.e.209.5 | 8 | 105.104 | even | 2 | inner | ||
1680.2.k.e.209.6 | 8 | 1.1 | even | 1 | trivial | ||
1680.2.k.f.209.3 | 8 | 5.4 | even | 2 | |||
1680.2.k.f.209.4 | 8 | 21.20 | even | 2 | |||
1680.2.k.f.209.5 | 8 | 3.2 | odd | 2 | |||
1680.2.k.f.209.6 | 8 | 35.34 | odd | 2 |