Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(289,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.s (of order \(3\), degree \(2\), 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: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 2.43956i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2016.865 |
Dual form | 2016.2.s.u.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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −1.60074 | − | 2.77256i | −0.715871 | − | 1.23992i | −0.962623 | − | 0.270846i | \(-0.912697\pi\) |
0.246752 | − | 0.969079i | \(-0.420637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.02398 | + | 2.43956i | −0.387027 | + | 0.922069i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12471 | − | 3.68011i | 0.640625 | − | 1.10959i | −0.344669 | − | 0.938724i | \(-0.612009\pi\) |
0.985293 | − | 0.170871i | \(-0.0546580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.15352 | −0.874629 | −0.437314 | − | 0.899309i | \(-0.644070\pi\) | ||||
−0.437314 | + | 0.899309i | \(0.644070\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.20147 | + | 3.81306i | −0.533935 | + | 0.924803i | 0.465279 | + | 0.885164i | \(0.345954\pi\) |
−0.999214 | + | 0.0396391i | \(0.987379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57676 | − | 2.73103i | −0.361734 | − | 0.626541i | 0.626513 | − | 0.779411i | \(-0.284482\pi\) |
−0.988246 | + | 0.152870i | \(0.951148\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.20147 | + | 3.81306i | 0.459039 | + | 0.795078i | 0.998910 | − | 0.0466689i | \(-0.0148606\pi\) |
−0.539872 | + | 0.841747i | \(0.681527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.62471 | + | 4.54614i | −0.524943 | + | 0.909227i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.20147 | −1.33728 | −0.668640 | − | 0.743586i | \(-0.733123\pi\) | ||||
−0.668640 | + | 0.743586i | \(0.733123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02398 | + | 1.77358i | −0.183912 | + | 0.318544i | −0.943209 | − | 0.332199i | \(-0.892209\pi\) |
0.759298 | + | 0.650744i | \(0.225543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.40294 | − | 1.06607i | 1.42036 | − | 0.180198i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.82618 | + | 8.35920i | 0.793420 | + | 1.37424i | 0.923838 | + | 0.382784i | \(0.125035\pi\) |
−0.130418 | + | 0.991459i | \(0.541632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4989 | 1.63964 | 0.819822 | − | 0.572618i | \(-0.194072\pi\) | ||||
0.819822 | + | 0.572618i | \(0.194072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.750575 | 0.114462 | 0.0572308 | − | 0.998361i | \(-0.481773\pi\) | ||||
0.0572308 | + | 0.998361i | \(0.481773\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.20147 | − | 2.08101i | −0.175253 | − | 0.303547i | 0.764996 | − | 0.644035i | \(-0.222741\pi\) |
−0.940249 | + | 0.340488i | \(0.889408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.90294 | − | 4.99611i | −0.700421 | − | 0.713730i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.64869 | + | 2.85561i | −0.226465 | + | 0.392249i | −0.956758 | − | 0.290885i | \(-0.906050\pi\) |
0.730293 | + | 0.683134i | \(0.239384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6044 | −1.83442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.12471 | − | 7.14421i | 0.536992 | − | 0.930097i | −0.462072 | − | 0.886842i | \(-0.652894\pi\) |
0.999064 | − | 0.0432549i | \(-0.0137727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.04795 | + | 7.01126i | 0.518287 | + | 0.897700i | 0.999774 | + | 0.0212466i | \(0.00676352\pi\) |
−0.481487 | + | 0.876453i | \(0.659903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.04795 | + | 8.74331i | 0.626121 | + | 1.08447i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.57676 | + | 4.46308i | −0.314801 | + | 0.545252i | −0.979395 | − | 0.201953i | \(-0.935271\pi\) |
0.664594 | + | 0.747205i | \(0.268605\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.40294 | −0.759890 | −0.379945 | − | 0.925009i | \(-0.624057\pi\) | ||||
−0.379945 | + | 0.925009i | \(0.624057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.62471 | + | 13.2064i | −0.892405 | + | 1.54569i | −0.0554215 | + | 0.998463i | \(0.517650\pi\) |
−0.836984 | + | 0.547228i | \(0.815683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.80221 | + | 8.95172i | 0.775184 | + | 1.02014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.22545 | + | 14.2469i | 0.925435 | + | 1.60290i | 0.790860 | + | 0.611998i | \(0.209634\pi\) |
0.134576 | + | 0.990903i | \(0.457033\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5565 | −1.59778 | −0.798890 | − | 0.601477i | \(-0.794579\pi\) | ||||
−0.798890 | + | 0.601477i | \(0.794579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.0959 | 1.52892 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.20147 | + | 2.08101i | 0.127356 | + | 0.220587i | 0.922651 | − | 0.385635i | \(-0.126018\pi\) |
−0.795296 | + | 0.606222i | \(0.792684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.22913 | − | 7.69321i | 0.338505 | − | 0.806468i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.04795 | + | 8.74331i | −0.517909 | + | 0.897045i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24943 | 0.431464 | 0.215732 | − | 0.976453i | \(-0.430786\pi\) | ||||
0.215732 | + | 0.976453i | \(0.430786\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.95205 | − | 3.38104i | 0.194236 | − | 0.336427i | −0.752414 | − | 0.658691i | \(-0.771111\pi\) |
0.946650 | + | 0.322264i | \(0.104444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.62471 | − | 8.01024i | −0.455686 | − | 0.789272i | 0.543041 | − | 0.839706i | \(-0.317273\pi\) |
−0.998727 | + | 0.0504341i | \(0.983940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.27823 | + | 14.3383i | 0.800287 | + | 1.38614i | 0.919427 | + | 0.393260i | \(0.128653\pi\) |
−0.119140 | + | 0.992877i | \(0.538014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0277 | + | 17.3684i | −0.960475 | + | 1.66359i | −0.239167 | + | 0.970979i | \(0.576874\pi\) |
−0.721309 | + | 0.692614i | \(0.756459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.04795 | − | 12.2074i | 0.657225 | − | 1.13835i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.04795 | − | 9.27512i | −0.646085 | − | 0.850249i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.52881 | − | 6.11207i | −0.320801 | − | 0.555643i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.798528 | 0.0714225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.4509 | 1.10484 | 0.552419 | − | 0.833566i | \(-0.313705\pi\) | ||||
0.552419 | + | 0.833566i | \(0.313705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.12471 | + | 3.68011i | 0.185637 | + | 0.321533i | 0.943791 | − | 0.330543i | \(-0.107232\pi\) |
−0.758154 | + | 0.652076i | \(0.773898\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.27708 | − | 1.05010i | 0.717714 | − | 0.0910551i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.20147 | + | 9.00921i | −0.444392 | + | 0.769709i | −0.998010 | − | 0.0630617i | \(-0.979914\pi\) |
0.553618 | + | 0.832771i | \(0.313247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6524 | 0.988341 | 0.494171 | − | 0.869365i | \(-0.335472\pi\) | ||||
0.494171 | + | 0.869365i | \(0.335472\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.70032 | + | 11.6053i | −0.560309 | + | 0.970484i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.5277 | + | 19.9665i | 0.957320 | + | 1.65813i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.20147 | + | 9.00921i | 0.426121 | + | 0.738064i | 0.996524 | − | 0.0833012i | \(-0.0265464\pi\) |
−0.570403 | + | 0.821365i | \(0.693213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0037 | − | 17.3269i | 0.814088 | − | 1.41004i | −0.0958929 | − | 0.995392i | \(-0.530571\pi\) |
0.909981 | − | 0.414650i | \(-0.136096\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.55646 | 0.526628 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.24943 | + | 12.5564i | −0.578567 | + | 1.00211i | 0.417077 | + | 0.908871i | \(0.363055\pi\) |
−0.995644 | + | 0.0932364i | \(0.970279\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.5565 | + | 1.46615i | −0.910777 | + | 0.115549i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.35499 | + | 9.27512i | 0.419435 | + | 0.726483i | 0.995883 | − | 0.0906510i | \(-0.0288948\pi\) |
−0.576447 | + | 0.817134i | \(0.695561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3047 | −1.33908 | −0.669540 | − | 0.742776i | \(-0.733509\pi\) | ||||
−0.669540 | + | 0.742776i | \(0.733509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.05531 | −0.235024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.95205 | − | 3.38104i | −0.148411 | − | 0.257056i | 0.782229 | − | 0.622991i | \(-0.214083\pi\) |
−0.930640 | + | 0.365935i | \(0.880749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.40294 | − | 11.0583i | −0.635203 | − | 0.835928i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4029 | − | 18.0184i | 0.777553 | − | 1.34676i | −0.155796 | − | 0.987789i | \(-0.549794\pi\) |
0.933349 | − | 0.358971i | \(-0.116872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2494 | −0.984822 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.4509 | − | 26.7617i | 1.13597 | − | 1.96756i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.35499 | + | 16.2033i | 0.684105 | + | 1.18490i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.09591 | + | 3.63021i | 0.151654 | + | 0.262673i | 0.931836 | − | 0.362880i | \(-0.118207\pi\) |
−0.780181 | + | 0.625553i | \(0.784873\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.15237 | − | 15.8524i | 0.658802 | − | 1.14108i | −0.322124 | − | 0.946697i | \(-0.604397\pi\) |
0.980926 | − | 0.194381i | \(-0.0622698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9041 | −0.848132 | −0.424066 | − | 0.905631i | \(-0.639397\pi\) | ||||
−0.424066 | + | 0.905631i | \(0.639397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.402945 | + | 0.697921i | −0.0285640 | + | 0.0494743i | −0.879954 | − | 0.475059i | \(-0.842427\pi\) |
0.851390 | + | 0.524533i | \(0.175760\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.37414 | − | 17.5685i | 0.517563 | − | 1.23306i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.8059 | − | 29.1087i | −1.17377 | − | 2.03304i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.4006 | −0.926942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.49885 | 0.585085 | 0.292542 | − | 0.956253i | \(-0.405499\pi\) | ||||
0.292542 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.20147 | − | 2.08101i | −0.0819397 | − | 0.141924i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.27823 | − | 4.31416i | −0.222541 | − | 0.292864i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.94239 | − | 12.0246i | 0.466995 | − | 0.808860i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7985 | −1.12491 | −0.562456 | − | 0.826827i | \(-0.690144\pi\) | ||||
−0.562456 | + | 0.826827i | \(0.690144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.43175 | + | 14.6042i | −0.559635 | + | 0.969316i | 0.437892 | + | 0.899028i | \(0.355725\pi\) |
−0.997527 | + | 0.0702885i | \(0.977608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.2771 | − | 17.8004i | −0.679129 | − | 1.17629i | −0.975244 | − | 0.221133i | \(-0.929024\pi\) |
0.296115 | − | 0.955152i | \(-0.404309\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.95205 | + | 8.57720i | 0.324419 | + | 0.561911i | 0.981395 | − | 0.192001i | \(-0.0614978\pi\) |
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.84648 | + | 6.66230i | −0.250917 | + | 0.434601i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.40294 | −0.284803 | −0.142401 | − | 0.989809i | \(-0.545482\pi\) | ||||
−0.142401 | + | 0.989809i | \(0.545482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4318 | + | 18.0683i | −0.671968 | + | 1.16388i | 0.305377 | + | 0.952232i | \(0.401218\pi\) |
−0.977345 | + | 0.211652i | \(0.932116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.00368 | + | 21.5911i | −0.383561 | + | 1.37941i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.97234 | + | 8.61235i | 0.316383 | + | 0.547991i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.44354 | −0.217354 | −0.108677 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108677 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.7100 | 1.17629 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.79853 | − | 4.84719i | −0.174567 | − | 0.302360i | 0.765444 | − | 0.643502i | \(-0.222519\pi\) |
−0.940011 | + | 0.341143i | \(0.889186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.3347 | + | 3.21417i | −1.57422 | + | 0.199719i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.798528 | + | 1.38309i | −0.0492393 | + | 0.0852850i | −0.889595 | − | 0.456751i | \(-0.849013\pi\) |
0.840355 | + | 0.542036i | \(0.182346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5565 | 0.648478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.85016 | − | 15.3289i | 0.539604 | − | 0.934621i | −0.459321 | − | 0.888270i | \(-0.651907\pi\) |
0.998925 | − | 0.0463511i | \(-0.0147593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.19779 | + | 2.07464i | 0.0727607 | + | 0.126025i | 0.900110 | − | 0.435662i | \(-0.143486\pi\) |
−0.827350 | + | 0.561687i | \(0.810152\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.1535 | + | 19.3185i | 0.672583 | + | 1.16495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62471 | − | 4.54614i | 0.157704 | − | 0.273151i | −0.776337 | − | 0.630319i | \(-0.782924\pi\) |
0.934040 | + | 0.357168i | \(0.116258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0959 | −1.19882 | −0.599411 | − | 0.800442i | \(-0.704598\pi\) | ||||
−0.599411 | + | 0.800442i | \(0.704598\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6247 | − | 20.1346i | 0.691017 | − | 1.19688i | −0.280487 | − | 0.959858i | \(-0.590496\pi\) |
0.971505 | − | 0.237020i | \(-0.0761706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7506 | + | 25.6126i | −0.634586 | + | 1.51186i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.19296 | − | 2.06627i | −0.0701742 | − | 0.121545i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2015 | −0.654397 | −0.327199 | − | 0.944956i | \(-0.606105\pi\) | ||||
−0.327199 | + | 0.944956i | \(0.606105\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.4103 | −1.53767 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.94239 | − | 12.0246i | −0.401489 | − | 0.695399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.768571 | + | 1.83108i | −0.0442997 | + | 0.105541i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9594 | − | 22.4464i | 0.742054 | − | 1.28527i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.9571 | −1.65267 | −0.826335 | − | 0.563179i | \(-0.809578\pi\) | ||||
−0.826335 | + | 0.563179i | \(0.809578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6524 | − | 23.6466i | 0.774155 | − | 1.34088i | −0.161113 | − | 0.986936i | \(-0.551508\pi\) |
0.935268 | − | 0.353940i | \(-0.115158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.74943 | + | 4.76214i | 0.155407 | + | 0.269172i | 0.933207 | − | 0.359339i | \(-0.116998\pi\) |
−0.777800 | + | 0.628511i | \(0.783665\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.80221 | − | 8.31767i | −0.269719 | − | 0.467167i | 0.699070 | − | 0.715053i | \(-0.253597\pi\) |
−0.968789 | + | 0.247886i | \(0.920264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.3011 | + | 26.5022i | −0.856695 | + | 1.48384i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.8848 | 0.772569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.27708 | − | 14.3363i | 0.459130 | − | 0.795236i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.30704 | − | 0.800162i | 0.347718 | − | 0.0441144i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.77823 | − | 13.4723i | −0.427530 | − | 0.740504i | 0.569123 | − | 0.822253i | \(-0.307283\pi\) |
−0.996653 | + | 0.0817484i | \(0.973950\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.4989 | 0.901428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.9977 | 0.980397 | 0.490199 | − | 0.871611i | \(-0.336924\pi\) | ||||
0.490199 | + | 0.871611i | \(0.336924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.35131 | + | 7.53669i | 0.235637 | + | 0.408135i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2088 | − | 6.84515i | 0.929190 | − | 0.369603i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.84648 | − | 4.93025i | 0.152807 | − | 0.264670i | −0.779451 | − | 0.626463i | \(-0.784502\pi\) |
0.932258 | + | 0.361793i | \(0.117835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1918 | −0.973785 | −0.486893 | − | 0.873462i | \(-0.661870\pi\) | ||||
−0.486893 | + | 0.873462i | \(0.661870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4989 | + | 18.1845i | −0.558797 | + | 0.967866i | 0.438800 | + | 0.898585i | \(0.355404\pi\) |
−0.997597 | + | 0.0692807i | \(0.977930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.2494 | + | 17.7525i | 0.543983 | + | 0.942206i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.3453 | − | 21.3827i | −0.651562 | − | 1.12854i | −0.982744 | − | 0.184971i | \(-0.940781\pi\) |
0.331182 | − | 0.943567i | \(-0.392552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.52766 | − | 7.84213i | 0.238298 | − | 0.412744i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 48.8206 | 2.55539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.92807 | − | 5.07157i | 0.152844 | − | 0.264734i | −0.779428 | − | 0.626492i | \(-0.784490\pi\) |
0.932272 | + | 0.361758i | \(0.117823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.27823 | − | 6.94616i | −0.274032 | − | 0.360627i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.317673 | − | 0.550227i | −0.0164485 | − | 0.0284897i | 0.857684 | − | 0.514177i | \(-0.171903\pi\) |
−0.874132 | + | 0.485688i | \(0.838569\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.7100 | 1.16962 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7506 | 0.552220 | 0.276110 | − | 0.961126i | \(-0.410955\pi\) | ||||
0.276110 | + | 0.961126i | \(0.410955\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.49885 | + | 12.9884i | 0.383173 | + | 0.663676i | 0.991514 | − | 0.130000i | \(-0.0414979\pi\) |
−0.608341 | + | 0.793676i | \(0.708165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9306 | − | 33.1888i | 0.709969 | − | 1.69146i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.10557 | − | 5.37900i | 0.157458 | − | 0.272726i | −0.776493 | − | 0.630126i | \(-0.783003\pi\) |
0.933952 | + | 0.357400i | \(0.116337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3859 | −0.980388 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.3335 | − | 45.6110i | 1.32498 | − | 2.29494i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.624713 | − | 1.08203i | −0.0313534 | − | 0.0543057i | 0.849923 | − | 0.526907i | \(-0.176648\pi\) |
−0.881276 | + | 0.472601i | \(0.843315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.05761 | + | 1.83184i | 0.0528147 | + | 0.0914778i | 0.891224 | − | 0.453563i | \(-0.149847\pi\) |
−0.838409 | + | 0.545041i | \(0.816514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.22913 | − | 5.59302i | 0.160854 | − | 0.278608i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.0170 | 2.03314 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.05646 | − | 13.9542i | 0.398367 | − | 0.689991i | −0.595158 | − | 0.803609i | \(-0.702911\pi\) |
0.993525 | + | 0.113618i | \(0.0362439\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.2052 | + | 17.3780i | 0.649783 | + | 0.855116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.3011 | + | 40.3586i | 1.14380 | + | 1.98113i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.1106 | 0.982469 | 0.491234 | − | 0.871027i | \(-0.336546\pi\) | ||||
0.491234 | + | 0.871027i | \(0.336546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.96171 | 0.241819 | 0.120909 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120909 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5565 | − | 20.0164i | −0.560571 | − | 0.970937i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.2494 | + | 2.69588i | −1.02833 | + | 0.130463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4029 | + | 18.0184i | −0.501092 | + | 0.867917i | 0.498907 | + | 0.866656i | \(0.333735\pi\) |
−0.999999 | + | 0.00126164i | \(0.999598\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.05531 | −0.387114 | −0.193557 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193557 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.94239 | − | 12.0246i | 0.332099 | − | 0.575213i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.09959 | + | 14.0289i | 0.386572 | + | 0.669563i | 0.991986 | − | 0.126348i | \(-0.0403257\pi\) |
−0.605414 | + | 0.795911i | \(0.706992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.72177 | + | 13.3745i | 0.366872 | + | 0.635441i | 0.989075 | − | 0.147415i | \(-0.0470953\pi\) |
−0.622202 | + | 0.782856i | \(0.713762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.84648 | − | 6.66230i | 0.182341 | − | 0.315823i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.5159 | −1.48733 | −0.743663 | − | 0.668555i | \(-0.766913\pi\) | ||||
−0.743663 | + | 0.668555i | \(0.766913\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3070 | − | 38.6369i | 1.05040 | − | 1.81934i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −26.4989 | + | 3.36186i | −1.24229 | + | 0.157606i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.55761 | + | 9.62607i | 0.259974 | + | 0.450289i | 0.966235 | − | 0.257664i | \(-0.0829526\pi\) |
−0.706260 | + | 0.707952i | \(0.749619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.5971 | −0.633278 | −0.316639 | − | 0.948546i | \(-0.602554\pi\) | ||||
−0.316639 | + | 0.948546i | \(0.602554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.55876 | 0.118916 | 0.0594579 | − | 0.998231i | \(-0.481063\pi\) | ||||
0.0594579 | + | 0.998231i | \(0.481063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.307039 | − | 0.531807i | −0.0142081 | − | 0.0246091i | 0.858834 | − | 0.512254i | \(-0.171189\pi\) |
−0.873042 | + | 0.487645i | \(0.837856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.24943 | − | 10.8563i | −0.380923 | − | 0.501295i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.59476 | − | 2.76220i | 0.0733270 | − | 0.127006i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.5542 | 0.759557 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0480 | − | 17.4036i | 0.459103 | − | 0.795189i | −0.539811 | − | 0.841786i | \(-0.681504\pi\) |
0.998914 | + | 0.0465970i | \(0.0148377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2195 | − | 26.3609i | −0.693948 | − | 1.20195i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.80221 | − | 11.7818i | −0.308872 | − | 0.534983i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6860 | + | 20.2408i | −0.529544 | + | 0.917196i | 0.469863 | + | 0.882740i | \(0.344303\pi\) |
−0.999406 | + | 0.0344568i | \(0.989030\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.7483 | −1.02662 | −0.513308 | − | 0.858205i | \(-0.671580\pi\) | ||||
−0.513308 | + | 0.858205i | \(0.671580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.8538 | − | 27.4597i | 0.714021 | − | 1.23672i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.55646 | − | 15.6204i | 0.294098 | − | 0.700670i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.26972 | + | 7.39537i | 0.191139 | + | 0.331062i | 0.945628 | − | 0.325250i | \(-0.105449\pi\) |
−0.754489 | + | 0.656313i | \(0.772115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.59706 | −0.338736 | −0.169368 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169368 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4989 | −0.556192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.49517 | − | 4.32176i | −0.110596 | − | 0.191559i | 0.805414 | − | 0.592712i | \(-0.201943\pi\) |
−0.916011 | + | 0.401153i | \(0.868609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.4103 | − | 32.1240i | −1.07985 | − | 1.42108i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.8059 | + | 25.6446i | −0.652425 | + | 1.13003i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2111 | −0.449085 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.24943 | + | 10.8243i | −0.273792 | + | 0.474222i | −0.969830 | − | 0.243783i | \(-0.921611\pi\) |
0.696037 | + | 0.718005i | \(0.254945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1309 | − | 38.3319i | −0.967718 | − | 1.67614i | −0.702129 | − | 0.712050i | \(-0.747767\pi\) |
−0.265589 | − | 0.964086i | \(-0.585566\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.50851 | − | 7.80897i | −0.196394 | − | 0.340164i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.80704 | − | 3.12988i | 0.0785669 | − | 0.136082i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.1083 | −1.43408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.5025 | − | 45.9037i | 1.14580 | − | 1.98459i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.8036 | + | 7.42807i | −1.24066 | + | 0.319950i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9797 | − | 22.4815i | −0.558041 | − | 0.966556i | −0.997660 | − | 0.0683711i | \(-0.978220\pi\) |
0.439619 | − | 0.898184i | \(-0.355114\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.2065 | 2.75031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9018 | 0.979210 | 0.489605 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489605 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3550 | + | 19.6674i | 0.483739 | + | 0.837860i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.1789 | + | 5.47802i | −1.83615 | + | 0.232949i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.25311 | + | 5.63454i | −0.137839 | + | 0.238743i | −0.926678 | − | 0.375856i | \(-0.877349\pi\) |
0.788840 | + | 0.614599i | \(0.210682\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.36695 | −0.100111 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.1224 | + | 38.3171i | −0.932349 | + | 1.61488i | −0.153053 | + | 0.988218i | \(0.548911\pi\) |
−0.779295 | + | 0.626657i | \(0.784423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.8059 | + | 22.1805i | 0.538748 | + | 0.933139i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.50851 | − | 11.2731i | −0.272851 | − | 0.472592i | 0.696740 | − | 0.717324i | \(-0.254633\pi\) |
−0.969591 | + | 0.244732i | \(0.921300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0853 | + | 26.1285i | −0.631299 | + | 1.09344i | 0.355987 | + | 0.934491i | \(0.384145\pi\) |
−0.987286 | + | 0.158951i | \(0.949189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.1129 | −0.963876 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9029 | − | 25.8127i | 0.620418 | − | 1.07459i | −0.368990 | − | 0.929433i | \(-0.620296\pi\) |
0.989408 | − | 0.145162i | \(-0.0463702\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9055 | − | 35.5114i | 0.618383 | − | 1.47326i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.00598 | + | 12.1347i | 0.290158 | + | 0.502568i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2494 | −0.753234 | −0.376617 | − | 0.926369i | \(-0.622913\pi\) | ||||
−0.376617 | + | 0.926369i | \(0.622913\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.45826 | 0.266108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8944 | − | 20.6018i | −0.488446 | − | 0.846013i | 0.511466 | − | 0.859304i | \(-0.329103\pi\) |
−0.999912 | + | 0.0132906i | \(0.995769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.4339 | + | 34.3879i | −0.591731 | + | 1.40976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.75057 | + | 13.4244i | −0.316680 | + | 0.548506i | −0.979793 | − | 0.200013i | \(-0.935901\pi\) |
0.663113 | + | 0.748519i | \(0.269235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8059 | 0.644736 | 0.322368 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322368 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.2974 | + | 19.5676i | −0.459304 | + | 0.795537i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.97602 | − | 5.15462i | −0.120793 | − | 0.209220i | 0.799288 | − | 0.600949i | \(-0.205210\pi\) |
−0.920081 | + | 0.391729i | \(0.871877\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.78887 | + | 6.56251i | 0.153281 | + | 0.265491i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.2015 | − | 24.5977i | 0.573592 | − | 0.993491i | −0.422601 | − | 0.906316i | \(-0.638883\pi\) |
0.996193 | − | 0.0871747i | \(-0.0277839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.1918 | 0.410307 | 0.205153 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205153 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4306 | + | 18.0663i | −0.419241 | + | 0.726147i | −0.995863 | − | 0.0908638i | \(-0.971037\pi\) |
0.576622 | + | 0.817011i | \(0.304371\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.30704 | + | 0.800162i | −0.252686 | + | 0.0320578i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8453 | + | 20.5167i | 0.473813 | + | 0.820669i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.4989 | −1.69454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.6191 | 1.65683 | 0.828416 | − | 0.560113i | \(-0.189242\pi\) | ||||
0.828416 | + | 0.560113i | \(0.189242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.9306 | − | 34.5208i | −0.790922 | − | 1.36992i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.4615 | + | 15.7553i | 0.612608 | + | 0.624249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4006 | + | 42.2632i | −0.963768 | + | 1.66929i | −0.250877 | + | 0.968019i | \(0.580719\pi\) |
−0.712890 | + | 0.701275i | \(0.752614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8442 | 0.467089 | 0.233544 | − | 0.972346i | \(-0.424968\pi\) | ||||
0.233544 | + | 0.972346i | \(0.424968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.7579 | − | 29.0256i | 0.658822 | − | 1.14111i | −0.322098 | − | 0.946706i | \(-0.604388\pi\) |
0.980921 | − | 0.194408i | \(-0.0622785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5277 | − | 30.3588i | −0.688021 | − | 1.19169i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.2531 | − | 40.2756i | −0.909964 | − | 1.57610i | −0.814111 | − | 0.580709i | \(-0.802775\pi\) |
−0.0958532 | − | 0.995395i | \(-0.530558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.80221 | − | 11.7818i | 0.265784 | − | 0.460352i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1152 | 0.394033 | 0.197017 | − | 0.980400i | \(-0.436875\pi\) | ||||
0.197017 | + | 0.980400i | \(0.436875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6321 | + | 28.8076i | −0.646913 | + | 1.12049i | 0.336943 | + | 0.941525i | \(0.390607\pi\) |
−0.983856 | + | 0.178961i | \(0.942726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.1609 | − | 21.2677i | −0.626692 | − | 0.824728i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.8538 | − | 27.4597i | −0.613863 | − | 1.06324i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4029 | 1.32811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.4966 | −1.94650 | −0.973249 | − | 0.229751i | \(-0.926209\pi\) | ||||
−0.973249 | + | 0.229751i | \(0.926209\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.3993 | + | 24.9403i | 0.553409 | + | 0.958532i | 0.998025 | + | 0.0628110i | \(0.0200065\pi\) |
−0.444617 | + | 0.895721i | \(0.646660\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.35131 | + | 10.3667i | −0.166988 | + | 0.397839i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.62356 | + | 11.4723i | −0.253444 | + | 0.438977i | −0.964472 | − | 0.264186i | \(-0.914897\pi\) |
0.711028 | + | 0.703164i | \(0.248230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.3047 | 1.27251 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.19917 | − | 9.00523i | 0.198073 | − | 0.343072i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8335 | + | 34.3527i | 0.754504 | + | 1.30684i | 0.945621 | + | 0.325271i | \(0.105456\pi\) |
−0.191117 | + | 0.981567i | \(0.561211\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.6524 | − | 32.3069i | −0.707525 | − | 1.22547i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.1129 | + | 40.0328i | −0.875465 | + | 1.51635i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.10787 | 0.0796130 | 0.0398065 | − | 0.999207i | \(-0.487326\pi\) | ||||
0.0398065 | + | 0.999207i | \(0.487326\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2195 | − | 26.3609i | 0.574013 | − | 0.994220i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.24943 | + | 8.22425i | 0.235034 | + | 0.309305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.49885 | + | 12.9884i | 0.281625 | + | 0.487789i | 0.971785 | − | 0.235868i | \(-0.0757932\pi\) |
−0.690160 | + | 0.723657i | \(0.742460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.01702 | −0.337690 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.9018 | 1.60444 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.4029 | + | 19.7505i | 0.425258 | + | 0.736569i | 0.996444 | − | 0.0842518i | \(-0.0268500\pi\) |
−0.571186 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.2771 | − | 3.07999i | 0.904126 | − | 0.114705i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.9018 | − | 32.7389i | 0.701995 | − | 1.21589i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9691 | 0.629348 | 0.314674 | − | 0.949200i | \(-0.398105\pi\) | ||||
0.314674 | + | 0.949200i | \(0.398105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.65237 | + | 2.86199i | −0.0611151 | + | 0.105854i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.672665 | − | 1.16509i | −0.0248455 | − | 0.0430336i | 0.853335 | − | 0.521362i | \(-0.174576\pi\) |
−0.878181 | + | 0.478329i | \(0.841243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.9497 | + | 18.9655i | 0.403339 | + | 0.698604i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6321 | + | 39.1999i | −0.832534 | + | 1.44199i | 0.0634880 | + | 0.997983i | \(0.479778\pi\) |
−0.896022 | + | 0.444009i | \(0.853556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.8036 | 1.02001 | 0.510007 | − | 0.860170i | \(-0.329643\pi\) | ||||
0.510007 | + | 0.860170i | \(0.329643\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.6524 | − | 28.8428i | 0.610096 | − | 1.05672i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.4560 | + | 5.51318i | −1.58785 | + | 0.201447i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0313 | − | 26.0350i | −0.548501 | − | 0.950032i | −0.998378 | − | 0.0569412i | \(-0.981865\pi\) |
0.449876 | − | 0.893091i | \(-0.351468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64.0530 | −2.33113 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3241 | −0.629654 | −0.314827 | − | 0.949149i | \(-0.601946\pi\) | ||||
−0.314827 | + | 0.949149i | \(0.601946\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.10557 | + | 10.5752i | 0.221327 | + | 0.383349i | 0.955211 | − | 0.295925i | \(-0.0956280\pi\) |
−0.733884 | + | 0.679274i | \(0.762295\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.1033 | − | 42.2480i | −1.16222 | − | 1.52948i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.0074 | + | 22.5294i | −0.469669 | + | 0.813490i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1152 | 0.400825 | 0.200413 | − | 0.979712i | \(-0.435772\pi\) | ||||
0.200413 | + | 0.979712i | \(0.435772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.143858 | + | 0.249170i | −0.00517423 | + | 0.00896202i | −0.868601 | − | 0.495512i | \(-0.834980\pi\) |
0.863427 | + | 0.504474i | \(0.168314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.37529 | − | 9.31027i | −0.193086 | − | 0.334435i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.5542 | − | 28.6727i | −0.593115 | − | 1.02730i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6044 | + | 23.5635i | −0.486804 | + | 0.843170i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.4177 | 1.65672 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.75057 | − | 9.96029i | 0.204986 | − | 0.355046i | −0.745142 | − | 0.666905i | \(-0.767618\pi\) |
0.950128 | + | 0.311860i | \(0.100952\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.19181 | − | 19.5165i | 0.291267 | − | 0.693927i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7653 | − | 22.1101i | −0.453309 | − | 0.785154i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.6980 | 0.662318 | 0.331159 | − | 0.943575i | \(-0.392560\pi\) | ||||
0.331159 | + | 0.943575i | \(0.392560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5800 | 0.374295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.4006 | + | 56.1196i | 1.14339 | + | 1.98042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.5638 | + | 29.6940i | 0.795270 | + | 1.04658i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.9018 | + | 46.5953i | −0.945817 | + | 1.63820i | −0.191709 | + | 0.981452i | \(0.561403\pi\) |
−0.754108 | + | 0.656751i | \(0.771930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.7866 | −1.22152 | −0.610761 | − | 0.791815i | \(-0.709136\pi\) | ||||
−0.610761 | + | 0.791815i | \(0.709136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.1439 | − | 29.6940i | 0.600523 | − | 1.04014i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.18348 | − | 2.04984i | −0.0414046 | − | 0.0717149i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9055 | + | 32.7452i | 0.659806 | + | 1.14282i | 0.980666 | + | 0.195690i | \(0.0626947\pi\) |
−0.320860 | + | 0.947127i | \(0.603972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.2088 | − | 47.1271i | 0.948440 | − | 1.64275i | 0.199728 | − | 0.979851i | \(-0.435994\pi\) |
0.748712 | − | 0.662896i | \(-0.230673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.86120 | 0.273361 | 0.136680 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136680 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.22913 | + | 5.59302i | −0.112152 | + | 0.194253i | −0.916638 | − | 0.399719i | \(-0.869108\pi\) |
0.804486 | + | 0.593972i | \(0.202441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.8442 | − | 7.69643i | 1.03404 | − | 0.266665i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7003 | + | 47.9784i | 0.958609 | + | 1.66036i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.3218 | 0.977776 | 0.488888 | − | 0.872347i | \(-0.337403\pi\) | ||||
0.488888 | + | 0.872347i | \(0.337403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8612 | 0.788317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.89075 | + | 8.47103i | 0.168247 | + | 0.291412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.5242 | − | 2.35013i | 0.636499 | − | 0.0807515i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2494 | + | 36.8051i | −0.728421 | + | 1.26166i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.75057 | 0.299614 | 0.149807 | − | 0.988715i | \(-0.452135\pi\) | ||||
0.149807 | + | 0.988715i | \(0.452135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.3453 | + | 21.3827i | −0.421708 | + | 0.730420i | −0.996107 | − | 0.0881555i | \(-0.971903\pi\) |
0.574398 | + | 0.818576i | \(0.305236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.24943 | + | 7.36022i | 0.144989 | + | 0.251127i | 0.929369 | − | 0.369153i | \(-0.120352\pi\) |
−0.784380 | + | 0.620280i | \(0.787019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.30704 | + | 16.1203i | 0.316815 | + | 0.548740i | 0.979822 | − | 0.199874i | \(-0.0640531\pi\) |
−0.663006 | + | 0.748614i | \(0.730720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.24943 | + | 10.8243i | −0.212487 | + | 0.368038i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 69.9069 | 2.37143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.12586 | − | 14.0744i | 0.275334 | − | 0.476893i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.817673 | + | 1.94806i | −0.0276424 | + | 0.0658564i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0553 | + | 38.2009i | 0.744755 | + | 1.28995i | 0.950309 | + | 0.311308i | \(0.100767\pi\) |
−0.205554 | + | 0.978646i | \(0.565900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.2900 | 0.380370 | 0.190185 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190185 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.2471 | −1.42173 | −0.710864 | − | 0.703329i | \(-0.751696\pi\) | ||||
−0.710864 | + | 0.703329i | \(0.751696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.99034 | − | 3.44737i | −0.0668290 | − | 0.115751i | 0.830675 | − | 0.556758i | \(-0.187955\pi\) |
−0.897504 | + | 0.441007i | \(0.854622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7494 | + | 30.3748i | −0.427602 | + | 1.01874i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.78887 | + | 6.56251i | −0.126790 | + | 0.219606i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −66.6095 | −2.22651 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.37414 | − | 12.7724i | 0.245941 | − | 0.425983i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.25909 | − | 12.5731i | −0.241835 | − | 0.418871i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.2088 | + | 36.7348i | 0.705005 | + | 1.22111i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.28674 | − | 10.8890i | 0.208748 | − | 0.361562i | −0.742572 | − | 0.669766i | \(-0.766395\pi\) |
0.951320 | + | 0.308204i | \(0.0997279\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.09821 | −0.235174 | −0.117587 | − | 0.993063i | \(-0.537516\pi\) | ||||
−0.117587 | + | 0.993063i | \(0.537516\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.9283 | + | 53.5694i | −1.02358 | + | 1.77289i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.1535 | + | 1.41503i | −0.368322 | + | 0.0467283i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.7206 | + | 32.4251i | 0.617536 | + | 1.06960i | 0.989934 | + | 0.141531i | \(0.0452024\pi\) |
−0.372398 | + | 0.928073i | \(0.621464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.1918 | 0.664622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.6694 | −1.66600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.94239 | + | 6.82841i | 0.129345 | + | 0.224033i | 0.923423 | − | 0.383783i | \(-0.125379\pi\) |
−0.794078 | + | 0.607816i | \(0.792046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.91376 | + | 21.2677i | −0.193816 | + | 0.697022i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9497 | − | 51.8745i | 0.979461 | − | 1.69648i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.9954 | 1.20859 | 0.604294 | − | 0.796762i | \(-0.293455\pi\) | ||||
0.604294 | + | 0.796762i | \(0.293455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.35131 | + | 11.0008i | −0.207047 | + | 0.358616i | −0.950783 | − | 0.309858i | \(-0.899719\pi\) |
0.743736 | + | 0.668473i | \(0.233052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1129 | + | 40.0328i | 0.752661 | + | 1.30365i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5565 | − | 20.0164i | −0.375535 | − | 0.650445i | 0.614872 | − | 0.788627i | \(-0.289208\pi\) |
−0.990407 | + | 0.138182i | \(0.955874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0447 | − | 41.6466i | 0.780523 | − | 1.35191i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4200 | 1.40651 | 0.703255 | − | 0.710937i | \(-0.251729\pi\) | ||||
0.703255 | + | 0.710937i | \(0.251729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.70998 | − | 11.6220i | 0.217130 | − | 0.376080i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.6524 | − | 21.9145i | −0.537733 | − | 0.707658i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4029 | + | 23.2146i | 0.432353 | + | 0.748857i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −58.6021 | −1.88647 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6450 | −0.374478 | −0.187239 | − | 0.982314i | \(-0.559954\pi\) | ||||
−0.187239 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.6812 | + | 28.8926i | 0.535324 | + | 0.927209i | 0.999148 | + | 0.0412813i | \(0.0131440\pi\) |
−0.463823 | + | 0.885928i | \(0.653523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.9318 | + | 28.4267i | −0.382514 | + | 0.911318i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.59476 | − | 16.6186i | 0.306963 | − | 0.531676i | −0.670733 | − | 0.741699i | \(-0.734020\pi\) |
0.977697 | + | 0.210023i | \(0.0673537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.2111 | 0.326349 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.03829 | − | 5.26248i | 0.0969065 | − | 0.167847i | −0.813496 | − | 0.581570i | \(-0.802439\pi\) |
0.910403 | + | 0.413723i | \(0.135772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.0553 | + | 33.0048i | 0.607153 | + | 1.05162i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.65237 | + | 2.86199i | 0.0525423 | + | 0.0910059i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8299 | + | 27.4181i | −0.502852 | + | 0.870966i | 0.497142 | + | 0.867669i | \(0.334383\pi\) |
−0.999995 | + | 0.00329664i | \(0.998951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.58003 | 0.0817925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.68003 | + | 13.3022i | −0.243229 | + | 0.421285i | −0.961632 | − | 0.274342i | \(-0.911540\pi\) |
0.718403 | + | 0.695627i | \(0.244873\pi\) | |||||||
\(998\) | 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 | 2016.2.s.u.865.1 | 6 | ||
3.2 | odd | 2 | 672.2.q.k.193.3 | ✓ | 6 | ||
4.3 | odd | 2 | 2016.2.s.v.865.1 | 6 | |||
7.2 | even | 3 | inner | 2016.2.s.u.289.1 | 6 | ||
12.11 | even | 2 | 672.2.q.l.193.3 | yes | 6 | ||
21.2 | odd | 6 | 672.2.q.k.289.3 | yes | 6 | ||
21.11 | odd | 6 | 4704.2.a.bu.1.1 | 3 | |||
21.17 | even | 6 | 4704.2.a.bt.1.3 | 3 | |||
24.5 | odd | 2 | 1344.2.q.z.193.1 | 6 | |||
24.11 | even | 2 | 1344.2.q.y.193.1 | 6 | |||
28.23 | odd | 6 | 2016.2.s.v.289.1 | 6 | |||
84.11 | even | 6 | 4704.2.a.bs.1.1 | 3 | |||
84.23 | even | 6 | 672.2.q.l.289.3 | yes | 6 | ||
84.59 | odd | 6 | 4704.2.a.bv.1.3 | 3 | |||
168.11 | even | 6 | 9408.2.a.ej.1.3 | 3 | |||
168.53 | odd | 6 | 9408.2.a.eh.1.3 | 3 | |||
168.59 | odd | 6 | 9408.2.a.eg.1.1 | 3 | |||
168.101 | even | 6 | 9408.2.a.ei.1.1 | 3 | |||
168.107 | even | 6 | 1344.2.q.y.961.1 | 6 | |||
168.149 | odd | 6 | 1344.2.q.z.961.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.k.193.3 | ✓ | 6 | 3.2 | odd | 2 | ||
672.2.q.k.289.3 | yes | 6 | 21.2 | odd | 6 | ||
672.2.q.l.193.3 | yes | 6 | 12.11 | even | 2 | ||
672.2.q.l.289.3 | yes | 6 | 84.23 | even | 6 | ||
1344.2.q.y.193.1 | 6 | 24.11 | even | 2 | |||
1344.2.q.y.961.1 | 6 | 168.107 | even | 6 | |||
1344.2.q.z.193.1 | 6 | 24.5 | odd | 2 | |||
1344.2.q.z.961.1 | 6 | 168.149 | odd | 6 | |||
2016.2.s.u.289.1 | 6 | 7.2 | even | 3 | inner | ||
2016.2.s.u.865.1 | 6 | 1.1 | even | 1 | trivial | ||
2016.2.s.v.289.1 | 6 | 28.23 | odd | 6 | |||
2016.2.s.v.865.1 | 6 | 4.3 | odd | 2 | |||
4704.2.a.bs.1.1 | 3 | 84.11 | even | 6 | |||
4704.2.a.bt.1.3 | 3 | 21.17 | even | 6 | |||
4704.2.a.bu.1.1 | 3 | 21.11 | odd | 6 | |||
4704.2.a.bv.1.3 | 3 | 84.59 | odd | 6 | |||
9408.2.a.eg.1.1 | 3 | 168.59 | odd | 6 | |||
9408.2.a.eh.1.3 | 3 | 168.53 | odd | 6 | |||
9408.2.a.ei.1.1 | 3 | 168.101 | even | 6 | |||
9408.2.a.ej.1.3 | 3 | 168.11 | even | 6 |