Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2640,2,Mod(1871,2640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2640.1871");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2640.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.0805061336\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.14786560000.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 43x^{4} + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1871.4 | ||
Root | \(1.67601 + 1.67601i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2640.1871 |
Dual form | 2640.2.k.c.1871.1 |
$q$-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 \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).
\(n\) | \(661\) | \(881\) | \(991\) | \(1057\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.61803 | + | 0.618034i | −0.934172 | + | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.07167i | 0.783016i | 0.920175 | + | 0.391508i | \(0.128046\pi\) | ||||
−0.920175 | + | 0.391508i | \(0.871954\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | − | 2.00000i | 0.745356 | − | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.58809 | 1.82721 | 0.913604 | − | 0.406605i | \(-0.133287\pi\) | ||||
0.913604 | + | 0.406605i | \(0.133287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | + | 1.61803i | 0.159576 | + | 0.417775i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.07167i | − | 0.987524i | −0.869597 | − | 0.493762i | \(-0.835621\pi\) | ||
0.869597 | − | 0.493762i | \(-0.164379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.18762i | − | 0.960706i | −0.877075 | − | 0.480353i | \(-0.840509\pi\) | ||
0.877075 | − | 0.480353i | \(-0.159491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.28036 | − | 3.35202i | −0.279397 | − | 0.731472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.70405 | −1.39789 | −0.698945 | − | 0.715175i | \(-0.746347\pi\) | ||||
−0.698945 | + | 0.715175i | \(0.746347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.38197 | + | 4.61803i | −0.458410 | + | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18762i | 0.406231i | 0.979155 | + | 0.203116i | \(0.0651067\pi\) | ||||
−0.979155 | + | 0.203116i | \(0.934893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.70405i | − | 1.56329i | −0.623721 | − | 0.781647i | \(-0.714380\pi\) | ||
0.623721 | − | 0.781647i | \(-0.285620\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61803 | − | 0.618034i | 0.281664 | − | 0.107586i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.07167 | 0.350175 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.61131 | −1.58009 | −0.790045 | − | 0.613049i | \(-0.789943\pi\) | ||||
−0.790045 | + | 0.613049i | \(0.789943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.6598 | + | 4.07167i | −1.70693 | + | 0.651988i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.18762i | 0.966344i | 0.875525 | + | 0.483172i | \(0.160515\pi\) | ||||
−0.875525 | + | 0.483172i | \(0.839485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2478i | 1.71528i | 0.514250 | + | 0.857641i | \(0.328070\pi\) | ||||
−0.514250 | + | 0.857641i | \(0.671930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | − | 2.23607i | −0.298142 | − | 0.333333i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.94012 | 1.44992 | 0.724958 | − | 0.688794i | \(-0.241859\pi\) | ||||
0.724958 | + | 0.688794i | \(0.241859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.70820 | 0.386886 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.51643 | + | 6.58809i | 0.352370 | + | 0.922517i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.94012i | − | 0.815938i | −0.912996 | − | 0.407969i | \(-0.866237\pi\) | ||
0.912996 | − | 0.407969i | \(-0.133763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000i | 0.134840i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.58809 | + | 6.77571i | 0.342801 | + | 0.897465i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.532019 | −0.0692630 | −0.0346315 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346315 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.704049 | 0.0901442 | 0.0450721 | − | 0.998984i | \(-0.485648\pi\) | ||||
0.0450721 | + | 0.998984i | \(0.485648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.14333 | + | 4.63238i | 0.522011 | + | 0.583626i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 6.58809i | − | 0.817152i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.14333i | − | 0.506188i | −0.967442 | − | 0.253094i | \(-0.918552\pi\) | ||
0.967442 | − | 0.253094i | \(-0.0814482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8474 | − | 4.14333i | 1.30587 | − | 0.498798i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.37940 | −0.638417 | −0.319209 | − | 0.947684i | \(-0.603417\pi\) | ||||
−0.319209 | + | 0.947684i | \(0.603417\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.25929 | −0.498512 | −0.249256 | − | 0.968438i | \(-0.580186\pi\) | ||||
−0.249256 | + | 0.968438i | \(0.580186\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.61803 | − | 0.618034i | 0.186834 | − | 0.0713644i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.07167i | − | 0.236088i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.9557i | − | 1.34512i | −0.740042 | − | 0.672561i | \(-0.765194\pi\) | ||
0.740042 | − | 0.672561i | \(-0.234806\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.25929 | 0.247989 | 0.123994 | − | 0.992283i | \(-0.460429\pi\) | ||||
0.123994 | + | 0.992283i | \(0.460429\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.07167 | −0.441634 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.35202 | − | 3.53965i | −0.144952 | − | 0.379490i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 17.5050i | − | 1.85553i | −0.373171 | − | 0.927763i | \(-0.621729\pi\) | ||
0.373171 | − | 0.927763i | \(-0.378271\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6483i | 1.43073i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.37940 | + | 14.0834i | 0.557818 | + | 1.46039i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.18762 | −0.429641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.85153 | 0.797202 | 0.398601 | − | 0.917124i | \(-0.369496\pi\) | ||||
0.398601 | + | 0.917124i | \(0.369496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.23607 | + | 2.00000i | −0.224733 | + | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.5712i | − | 1.25088i | −0.780273 | − | 0.625439i | \(-0.784920\pi\) | ||
0.780273 | − | 0.625439i | \(-0.215080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.94427i | − | 0.881305i | −0.897678 | − | 0.440653i | \(-0.854747\pi\) | ||
0.897678 | − | 0.440653i | \(-0.145253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.35202 | + | 1.28036i | −0.327124 | + | 0.124950i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.68499 | 0.259567 | 0.129784 | − | 0.991542i | \(-0.458572\pi\) | ||||
0.129784 | + | 0.991542i | \(0.458572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3752 | −0.993768 | −0.496884 | − | 0.867817i | \(-0.665523\pi\) | ||||
−0.496884 | + | 0.867817i | \(0.665523\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.5514 | − | 5.94012i | 1.47608 | − | 0.563811i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.6196i | − | 1.28123i | −0.767864 | − | 0.640613i | \(-0.778680\pi\) | ||
0.767864 | − | 0.640613i | \(-0.221320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.70405i | 0.625156i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.7314 | − | 13.1762i | 1.36192 | − | 1.21814i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.43513 | 0.773247 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.82416 | − | 10.0118i | −0.344813 | − | 0.902732i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0717i | 0.893716i | 0.894605 | + | 0.446858i | \(0.147457\pi\) | ||||
−0.894605 | + | 0.446858i | \(0.852543\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.95155 | − | 18.1994i | −0.612050 | − | 1.60237i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.61547 | −0.228514 | −0.114257 | − | 0.993451i | \(-0.536449\pi\) | ||||
−0.114257 | + | 0.993451i | \(0.536449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.67535 | 0.752248 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.61803 | + | 2.38197i | 0.397457 | + | 0.205007i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 19.4081i | − | 1.65815i | −0.559141 | − | 0.829073i | \(-0.688869\pi\) | ||
0.559141 | − | 0.829073i | \(-0.311131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.04429i | − | 0.682308i | −0.940007 | − | 0.341154i | \(-0.889182\pi\) | ||
0.940007 | − | 0.341154i | \(-0.110818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0834 | + | 6.14333i | −1.35447 | + | 0.517362i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.58809 | −0.550924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18762 | 0.181672 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.38197 | + | 1.67376i | −0.361418 | + | 0.138050i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.9793i | 1.47292i | 0.676481 | + | 0.736460i | \(0.263504\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.9886i | − | 1.05699i | −0.848935 | − | 0.528497i | \(-0.822756\pi\) | ||
0.848935 | − | 0.528497i | \(-0.177244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.14333 | − | 9.10452i | −0.658349 | − | 0.736057i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.70405 | −0.699126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6483 | 1.72772 | 0.863862 | − | 0.503728i | \(-0.168039\pi\) | ||||
0.863862 | + | 0.503728i | \(0.168039\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.67119 | + | 9.61131i | 0.291145 | + | 0.762227i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.8885i | − | 1.09457i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.0000i | − | 0.939913i | −0.882690 | − | 0.469956i | \(-0.844270\pi\) | ||
0.882690 | − | 0.469956i | \(-0.155730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.618034 | − | 1.61803i | −0.0481139 | − | 0.125964i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.5324 | 1.97575 | 0.987877 | − | 0.155240i | \(-0.0496150\pi\) | ||||
0.987877 | + | 0.155240i | \(0.0496150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.4030 | 2.33869 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.37524 | − | 9.36381i | −0.640471 | − | 0.716068i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5767i | 0.880157i | 0.897959 | + | 0.440078i | \(0.145049\pi\) | ||||
−0.897959 | + | 0.440078i | \(0.854951\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.07167i | − | 0.156603i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.860825 | − | 0.328806i | 0.0647036 | − | 0.0247146i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.7917 | −1.03084 | −0.515418 | − | 0.856939i | \(-0.672363\pi\) | ||||
−0.515418 | + | 0.856939i | \(0.672363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9949 | −1.78352 | −0.891762 | − | 0.452505i | \(-0.850531\pi\) | ||||
−0.891762 | + | 0.452505i | \(0.850531\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.13918 | + | 0.435126i | −0.0842102 | + | 0.0321655i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.61131i | 0.706638i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.07167i | 0.297750i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.56702 | − | 4.93464i | −0.695898 | − | 0.358942i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.560719 | −0.0405722 | −0.0202861 | − | 0.999794i | \(-0.506458\pi\) | ||||
−0.0202861 | + | 0.999794i | \(0.506458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.26858 | −0.379241 | −0.189620 | − | 0.981858i | \(-0.560726\pi\) | ||||
−0.189620 | + | 0.981858i | \(0.560726\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.07167 | + | 10.6598i | 0.291578 | + | 0.763361i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.3355i | 1.59134i | 0.605734 | + | 0.795668i | \(0.292880\pi\) | ||||
−0.605734 | + | 0.795668i | \(0.707120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.375243i | 0.0266003i | 0.999912 | + | 0.0133001i | \(0.00423369\pi\) | ||||
−0.999912 | + | 0.0133001i | \(0.995766\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.56072 | + | 6.70405i | 0.180619 | + | 0.472867i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.53202 | −0.318085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.18762 | 0.432162 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9907 | + | 13.4081i | −1.04193 | + | 0.931927i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.18762i | 0.289664i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.1647i | − | 1.52588i | −0.646467 | − | 0.762942i | \(-0.723754\pi\) | ||
0.646467 | − | 0.762942i | \(-0.276246\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.70405 | − | 3.32465i | 0.596392 | − | 0.227801i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.2478 | 0.767097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0319 | 1.22408 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.89167 | − | 2.63238i | 0.465696 | − | 0.177880i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 26.8245i | − | 1.80441i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.8432i | − | 0.927011i | −0.886094 | − | 0.463505i | \(-0.846591\pi\) | ||
0.886094 | − | 0.463505i | \(-0.153409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.23607 | + | 2.00000i | −0.149071 | + | 0.133333i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.8190 | 1.71367 | 0.856834 | − | 0.515592i | \(-0.172428\pi\) | ||||
0.856834 | + | 0.515592i | \(0.172428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.88023 | −0.520741 | −0.260370 | − | 0.965509i | \(-0.583845\pi\) | ||||
−0.260370 | + | 0.965509i | \(0.583845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.28036 | + | 3.35202i | 0.0842415 | + | 0.220547i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.96119i | 0.325018i | 0.986707 | + | 0.162509i | \(0.0519587\pi\) | ||||
−0.986707 | + | 0.162509i | \(0.948041\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.94012i | − | 0.648422i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.38903 | + | 19.3447i | 0.479969 | + | 1.25658i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.143330 | −0.00927125 | −0.00463563 | − | 0.999989i | \(-0.501476\pi\) | ||||
−0.00463563 | + | 0.999989i | \(0.501476\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8895 | −0.701456 | −0.350728 | − | 0.936477i | \(-0.614066\pi\) | ||||
−0.350728 | + | 0.936477i | \(0.614066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.90983 | + | 15.0902i | 0.250816 | + | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.70820i | − | 0.173021i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 27.5884i | − | 1.75541i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.65560 | + | 1.39632i | −0.231664 | + | 0.0884879i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1939 | 0.706554 | 0.353277 | − | 0.935519i | \(-0.385067\pi\) | ||||
0.353277 | + | 0.935519i | \(0.385067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.70405 | 0.421480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.58809 | − | 2.51643i | 0.412562 | − | 0.157585i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.26477i | 0.203651i | 0.994802 | + | 0.101825i | \(0.0324683\pi\) | ||||
−0.994802 | + | 0.101825i | \(0.967532\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.9114i | − | 1.23724i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.37524 | + | 4.89167i | 0.270821 | + | 0.302787i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7872 | 0.726827 | 0.363413 | − | 0.931628i | \(-0.381611\pi\) | ||||
0.363413 | + | 0.931628i | \(0.381611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.94012 | −0.364898 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8187 | + | 28.3237i | 0.662092 | + | 1.73338i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.06404i | 0.0648755i | 0.999474 | + | 0.0324378i | \(0.0103271\pi\) | ||||
−0.999474 | + | 0.0324378i | \(0.989673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.63521i | − | 0.463806i | −0.972739 | − | 0.231903i | \(-0.925505\pi\) | ||
0.972739 | − | 0.231903i | \(-0.0744952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.43513 | − | 22.0834i | −0.510517 | − | 1.33655i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4912 | 0.990860 | 0.495430 | − | 0.868648i | \(-0.335010\pi\) | ||||
0.495430 | + | 0.868648i | \(0.335010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.4081 | − | 19.4628i | −1.04220 | − | 1.16521i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.2112i | − | 1.32501i | −0.749058 | − | 0.662504i | \(-0.769494\pi\) | ||
0.749058 | − | 0.662504i | \(-0.230506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.78500i | − | 0.581658i | −0.956775 | − | 0.290829i | \(-0.906069\pi\) | ||
0.956775 | − | 0.290829i | \(-0.0939311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.77571 | − | 2.58809i | 0.401359 | − | 0.153305i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8187 | −0.756663 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.421544 | 0.0247967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.7040 | + | 4.85251i | −0.744725 | + | 0.284459i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.1510i | − | 1.11881i | −0.828894 | − | 0.559405i | \(-0.811030\pi\) | ||
0.828894 | − | 0.559405i | \(-0.188970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.532019i | 0.0309753i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.38197 | − | 4.61803i | 0.138216 | − | 0.267966i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −44.1669 | −2.55424 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3018 | −1.34309 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.76941 | + | 20.3406i | 0.446341 | + | 1.16854i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.704049i | − | 0.0403137i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.7200i | 0.783041i | 0.920169 | + | 0.391520i | \(0.128051\pi\) | ||||
−0.920169 | + | 0.391520i | \(0.871949\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.52786 | + | 14.4721i | 0.314469 | + | 0.823291i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.3565 | −0.757379 | −0.378690 | − | 0.925524i | \(-0.623625\pi\) | ||||
−0.378690 | + | 0.925524i | \(0.623625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7327 | −0.832744 | −0.416372 | − | 0.909194i | \(-0.636699\pi\) | ||||
−0.416372 | + | 0.909194i | \(0.636699\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.63238 | − | 4.14333i | 0.261005 | − | 0.233450i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.14749i | 0.176780i | 0.996086 | + | 0.0883902i | \(0.0281722\pi\) | ||||
−0.996086 | + | 0.0883902i | \(0.971828\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.18762i | − | 0.122483i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.34440 | + | 1.65941i | −0.242481 | + | 0.0926194i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.0506 | −0.948720 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.58809 | −0.365442 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.7875 | − | 6.41225i | 0.928351 | − | 0.354598i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.5926i | 1.13531i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.08760i | 0.389570i | 0.980846 | + | 0.194785i | \(0.0624009\pi\) | ||||
−0.980846 | + | 0.194785i | \(0.937599\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.4915 | + | 19.2226i | −1.17773 | + | 1.05339i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.14333 | −0.226374 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.5324 | 1.28189 | 0.640945 | − | 0.767587i | \(-0.278543\pi\) | ||||
0.640945 | + | 0.767587i | \(0.278543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.41739 | + | 22.0370i | 0.457170 | + | 1.19689i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.70405i | 0.471351i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1121i | 1.08595i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.14333 | − | 10.8474i | −0.223069 | − | 0.584003i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.46665 | 0.400831 | 0.200416 | − | 0.979711i | \(-0.435771\pi\) | ||||
0.200416 | + | 0.979711i | \(0.435771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.135020 | 0.00722746 | 0.00361373 | − | 0.999993i | \(-0.498850\pi\) | ||||
0.00361373 | + | 0.999993i | \(0.498850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6926 | + | 30.4240i | −0.837610 | + | 1.62391i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.13390i | − | 0.326475i | −0.986587 | − | 0.163237i | \(-0.947806\pi\) | ||
0.986587 | − | 0.163237i | \(-0.0521936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.37940i | 0.285509i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.6483 | + | 5.21319i | −0.722346 | + | 0.275912i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.9350 | 1.05213 | 0.526064 | − | 0.850445i | \(-0.323667\pi\) | ||||
0.526064 | + | 0.850445i | \(0.323667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.46383 | 0.0770435 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.61803 | + | 0.618034i | −0.0849248 | + | 0.0324384i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.25929i | 0.222941i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0286998i | 0.00149812i | 1.00000 | 0.000749058i | \(0.000238433\pi\) | |||||
−1.00000 | 0.000749058i | \(0.999762\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.3752 | + | 13.8359i | 0.644229 | + | 0.720270i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.3059 | 0.638892 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.70953 | 0.399184 | 0.199592 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199592 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.618034 | − | 1.61803i | −0.0319151 | − | 0.0835549i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4123i | 0.742269i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.8802i | − | 0.815713i | −0.913046 | − | 0.407856i | \(-0.866276\pi\) | ||
0.913046 | − | 0.407856i | \(-0.133724\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.22463 | − | 16.2963i | −0.318898 | − | 0.834885i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.88023 | 0.198271 | 0.0991353 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991353 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.07167 | −0.105582 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.4957 | + | 25.1510i | 1.14352 | + | 1.27849i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3836i | 0.729275i | 0.931150 | + | 0.364638i | \(0.118807\pi\) | ||||
−0.931150 | + | 0.364638i | \(0.881193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.2966i | 1.38045i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.23191 | − | 1.61645i | 0.213472 | − | 0.0815390i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.9557 | −0.601557 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0927 | 0.657106 | 0.328553 | − | 0.944486i | \(-0.393439\pi\) | ||||
0.328553 | + | 0.944486i | \(0.393439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.0370 | + | 5.36166i | −0.702729 | + | 0.268419i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8145i | 0.589989i | 0.955499 | + | 0.294995i | \(0.0953179\pi\) | ||||
−0.955499 | + | 0.294995i | \(0.904682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 57.3431i | − | 2.85646i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.94427 | − | 1.00000i | −0.444444 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.61131 | 0.476415 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.8885 | 1.18121 | 0.590606 | − | 0.806960i | \(-0.298889\pi\) | ||||
0.590606 | + | 0.806960i | \(0.298889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9949 | + | 31.4030i | 0.591663 | + | 1.54899i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.10217i | − | 0.0542340i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.25929i | − | 0.110904i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.97165 | + | 13.0159i | 0.243463 | + | 0.637393i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7276 | 1.40344 | 0.701718 | − | 0.712455i | \(-0.252417\pi\) | ||||
0.701718 | + | 0.712455i | \(0.252417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5967 | −0.857613 | −0.428807 | − | 0.903396i | \(-0.641066\pi\) | ||||
−0.428807 | + | 0.903396i | \(0.641066\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.2268 | − | 19.8802i | 1.08070 | − | 0.966610i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.07167i | 0.197505i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.45855i | 0.0705844i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.6598 | − | 4.07167i | 0.514658 | − | 0.196582i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.37524 | 0.210748 | 0.105374 | − | 0.994433i | \(-0.466396\pi\) | ||||
0.105374 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.21418 | 0.298634 | 0.149317 | − | 0.988789i | \(-0.452292\pi\) | ||||
0.149317 | + | 0.988789i | \(0.452292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.53965 | + | 1.35202i | −0.169713 | + | 0.0648246i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.0740i | 1.34296i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 11.4753i | − | 0.547684i | −0.961775 | − | 0.273842i | \(-0.911705\pi\) | ||
0.961775 | − | 0.273842i | \(-0.0882946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.05573 | − | 5.41641i | 0.288368 | − | 0.257924i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.9897 | −1.70992 | −0.854962 | − | 0.518691i | \(-0.826420\pi\) | ||||
−0.854962 | + | 0.518691i | \(0.826420\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.5050 | −0.829816 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.1118 | − | 29.0911i | −0.525570 | − | 1.37596i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.9771i | 0.754007i | 0.926212 | + | 0.377004i | \(0.123046\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.18762i | − | 0.291364i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.02737 | + | 21.0159i | 0.377159 | + | 0.987415i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.6483 | 0.639843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4819 | −1.47266 | −0.736331 | − | 0.676622i | \(-0.763443\pi\) | ||||
−0.736331 | + | 0.676622i | \(0.763443\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.8031 | + | 9.69857i | 0.877653 | + | 0.452690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1007i | 1.44850i | 0.689535 | + | 0.724252i | \(0.257815\pi\) | ||||
−0.689535 | + | 0.724252i | \(0.742185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8515i | 1.10847i | 0.832359 | + | 0.554237i | \(0.186990\pi\) | ||||
−0.832359 | + | 0.554237i | \(0.813010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.0834 | − | 5.37940i | 0.653104 | − | 0.249464i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.5843 | −1.41527 | −0.707636 | − | 0.706577i | \(-0.750238\pi\) | ||||
−0.707636 | + | 0.706577i | \(0.750238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.58359 | 0.396353 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.0277 | + | 13.3794i | −1.61399 | + | 0.616490i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 11.2478i | − | 0.517177i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.18762i | 0.192141i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.8802 | − | 13.2825i | −0.543959 | − | 0.608164i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8895 | −0.588937 | −0.294469 | − | 0.955661i | \(-0.595143\pi\) | ||||
−0.294469 | + | 0.955661i | \(0.595143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −63.3202 | −2.88715 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.58359 | + | 22.4721i | 0.390567 | + | 1.02252i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.85153i | − | 0.356520i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.5597i | 1.06759i | 0.845613 | + | 0.533797i | \(0.179235\pi\) | ||||
−0.845613 | + | 0.533797i | \(0.820765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.41641 | + | 19.4164i | 0.335382 | + | 0.878040i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.93596 | −0.313016 | −0.156508 | − | 0.987677i | \(-0.550024\pi\) | ||||
−0.156508 | + | 0.987677i | \(0.550024\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.90726 | 0.401163 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | + | 2.23607i | 0.0898933 | + | 0.100504i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.1443i | − | 0.499891i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.282369i | − | 0.0126406i | −0.999980 | − | 0.00632028i | \(-0.997988\pi\) | ||
0.999980 | − | 0.00632028i | \(-0.00201182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.3122 | + | 15.7799i | −1.84569 | + | 0.704993i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.1952 | −1.83681 | −0.918403 | − | 0.395647i | \(-0.870520\pi\) | ||||
−0.918403 | + | 0.395647i | \(0.870520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.5712 | −0.559410 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −49.1930 | + | 18.7901i | −2.18474 | + | 0.834496i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 26.8162i | − | 1.18861i | −0.804241 | − | 0.594303i | \(-0.797428\pi\) | ||
0.804241 | − | 0.594303i | \(-0.202572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.82382i | − | 0.390343i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.3386 | + | 9.97477i | 0.853819 | + | 0.440397i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.94427 | −0.394132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.94012 | −0.437166 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.15477 | − | 18.7314i | −0.314059 | − | 0.822218i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3998i | 0.762299i | 0.924514 | + | 0.381149i | \(0.124472\pi\) | ||||
−0.924514 | + | 0.381149i | \(0.875528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 30.1838i | − | 1.31985i | −0.751333 | − | 0.659923i | \(-0.770589\pi\) | ||
0.751333 | − | 0.659923i | \(-0.229411\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.28036 | + | 3.35202i | 0.0558795 | + | 0.146294i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.4400 | −1.54379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.9443 | 0.954099 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.18963 | + | 1.06404i | −0.0516256 | + | 0.0461753i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.7646i | 1.76571i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.68499i | − | 0.116082i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.3154 | − | 8.52371i | 0.962979 | − | 0.367825i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.70820 | −0.116651 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.79165 | −0.420976 | −0.210488 | − | 0.977596i | \(-0.567505\pi\) | ||||
−0.210488 | + | 0.977596i | \(0.567505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.8245 | − | 14.8296i | 1.66612 | − | 0.636401i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.3752i | 0.444427i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.1686i | − | 0.862345i | −0.902269 | − | 0.431173i | \(-0.858100\pi\) | ||
0.902269 | − | 0.431173i | \(-0.141900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.57430 | − | 1.40810i | 0.0671895 | − | 0.0600962i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.16093 | 0.390269 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.7682 | 1.05325 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.94012 | − | 15.5514i | −0.252144 | − | 0.660121i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.5262i | 1.33581i | 0.744247 | + | 0.667904i | \(0.232808\pi\) | ||||
−0.744247 | + | 0.667904i | \(0.767192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 74.1019i | 3.13418i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.51643 | − | 6.58809i | −0.106244 | − | 0.278149i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.1160 | −0.594917 | −0.297458 | − | 0.954735i | \(-0.596139\pi\) | ||||
−0.297458 | + | 0.954735i | \(0.596139\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6196 | −0.572982 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.5295 | + | 2.07167i | 0.778167 | + | 0.0870018i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.2195i | 0.679957i | 0.940433 | + | 0.339978i | \(0.110420\pi\) | ||||
−0.940433 | + | 0.339978i | \(0.889580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.50714i | − | 0.0630717i | −0.999503 | − | 0.0315358i | \(-0.989960\pi\) | ||
0.999503 | − | 0.0315358i | \(-0.0100398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.907262 | − | 0.346543i | 0.0379014 | − | 0.0144771i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.70405 | 0.279578 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.646649 | −0.0269204 | −0.0134602 | − | 0.999909i | \(-0.504285\pi\) | ||||
−0.0134602 | + | 0.999909i | \(0.504285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.52474 | − | 3.25616i | 0.354276 | − | 0.135321i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.68049i | 0.194179i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.94012i | 0.246015i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.1762 | − | 14.7314i | −0.544768 | − | 0.609069i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.9907 | −0.618733 | −0.309366 | − | 0.950943i | \(-0.600117\pi\) | ||||
−0.309366 | + | 0.950943i | \(0.600117\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.4493 | −1.50187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.8041 | − | 36.1395i | −0.567824 | − | 1.48658i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23.4715i | − | 0.963857i | −0.876211 | − | 0.481929i | \(-0.839936\pi\) | ||
0.876211 | − | 0.481929i | \(-0.160064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 8.43513i | − | 0.345806i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.231913 | − | 0.607156i | −0.00949157 | − | 0.0248492i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.0000 | 0.817178 | 0.408589 | − | 0.912719i | \(-0.366021\pi\) | ||||
0.408589 | + | 0.912719i | \(0.366021\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5597 | −0.716277 | −0.358138 | − | 0.933669i | \(-0.616588\pi\) | ||||
−0.358138 | + | 0.933669i | \(0.616588\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.28666 | − | 9.26477i | −0.337459 | − | 0.377291i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.00000i | − | 0.0406558i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.19310i | − | 0.291959i | −0.989288 | − | 0.145980i | \(-0.953367\pi\) | ||
0.989288 | − | 0.145980i | \(-0.0466334\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.33296 | − | 2.80094i | 0.297147 | − | 0.113500i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 65.4864 | 2.64930 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.2583 | −1.02017 | −0.510087 | − | 0.860123i | \(-0.670387\pi\) | ||||
−0.510087 | + | 0.860123i | \(0.670387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.0118 | + | 3.82416i | −0.403714 | + | 0.154205i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 30.8339i | − | 1.24133i | −0.784077 | − | 0.620664i | \(-0.786863\pi\) | ||
0.784077 | − | 0.620664i | \(-0.213137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.4483i | 1.42479i | 0.701780 | + | 0.712393i | \(0.252389\pi\) | ||||
−0.701780 | + | 0.712393i | \(0.747611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.9688 | − | 30.9595i | 0.640807 | − | 1.24236i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.2645 | 1.45291 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.58809 | − | 6.77571i | −0.103358 | − | 0.270596i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.1340i | 1.56038i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 44.2555i | − | 1.76178i | −0.473319 | − | 0.880891i | \(-0.656944\pi\) | ||
0.473319 | − | 0.880891i | \(-0.343056\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.6986 | + | 35.8633i | 0.544469 | + | 1.42544i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0717 | 0.399682 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8419 | 0.706922 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0287 | + | 10.7588i | −0.475848 | + | 0.425611i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 38.6162i | − | 1.52525i | −0.646843 | − | 0.762623i | \(-0.723911\pi\) | ||
0.646843 | − | 0.762623i | \(-0.276089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.53617i | − | 0.139453i | −0.997566 | − | 0.0697265i | \(-0.977787\pi\) | ||
0.997566 | − | 0.0697265i | \(-0.0222127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.1994 | + | 6.95155i | −0.716601 | + | 0.273717i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.8245 | −1.29046 | −0.645232 | − | 0.763986i | \(-0.723239\pi\) | ||||
−0.645232 | + | 0.763986i | \(0.723239\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.532019 | 0.0208836 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.1762 | + | 11.1443i | −1.14350 | + | 0.436780i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1516i | 0.475530i | 0.971323 | + | 0.237765i | \(0.0764149\pi\) | ||||
−0.971323 | + | 0.237765i | \(0.923585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.61547i | 0.102195i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.52405 | + | 8.51857i | −0.371569 | + | 0.332341i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5936 | −0.607439 | −0.303720 | − | 0.952761i | \(-0.598229\pi\) | ||||
−0.303720 | + | 0.952761i | \(0.598229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.35901 | −0.364023 | −0.182012 | − | 0.983296i | \(-0.558261\pi\) | ||||
−0.182012 | + | 0.983296i | \(0.558261\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.5785 | + | 43.4030i | 0.643854 | + | 1.68563i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.67535i | − | 0.336416i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.6659i | − | 0.567867i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.55558 | + | 22.3988i | 0.330778 | + | 0.865988i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.704049 | −0.0271795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.0426 | −1.31225 | −0.656123 | − | 0.754654i | \(-0.727805\pi\) | ||||
−0.656123 | + | 0.754654i | \(0.727805\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.38197 | − | 4.61803i | 0.0916819 | − | 0.177748i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.1447i | 1.27385i | 0.770924 | + | 0.636927i | \(0.219795\pi\) | ||||
−0.770924 | + | 0.636927i | \(0.780205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.2657i | 0.624222i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.7761 | + | 15.9570i | −1.60086 | + | 0.611475i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.0330 | 1.30224 | 0.651118 | − | 0.758976i | \(-0.274300\pi\) | ||||
0.651118 | + | 0.758976i | \(0.274300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.4081 | −0.741545 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.7505 | − | 4.87025i | 0.486461 | − | 0.185812i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 39.1340i | − | 1.49089i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.2226i | 0.579096i | 0.957164 | + | 0.289548i | \(0.0935050\pi\) | ||||
−0.957164 | + | 0.289548i | \(0.906495\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.14333 | − | 4.63238i | −0.157392 | − | 0.175970i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.04429 | −0.305137 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.1939 | 0.954288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.06618 | − | 8.02737i | −0.115974 | − | 0.303623i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.90096i | 0.373954i | 0.982364 | + | 0.186977i | \(0.0598690\pi\) | ||||
−0.982364 | + | 0.186977i | \(0.940131\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.2485i | 1.51800i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.14333 | + | 16.0834i | 0.231371 | + | 0.605738i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.0433 | 0.979458 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4687 | 1.55739 | 0.778694 | − | 0.627403i | \(-0.215882\pi\) | ||||
0.778694 | + | 0.627403i | \(0.215882\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.9114 | − | 26.7338i | −0.896748 | − | 1.00259i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 58.3524i | 2.18531i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.58809i | 0.246381i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.231913 | − | 0.0885829i | 0.00866095 | − | 0.00330819i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.1626 | 0.677351 | 0.338675 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338675 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.5295 | 0.690076 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6196 | − | 6.73010i | 0.655281 | − | 0.250295i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.18762i | − | 0.0812462i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 45.4030i | − | 1.68390i | −0.539553 | − | 0.841951i | \(-0.681407\pi\) | ||
0.539553 | − | 0.841951i | \(-0.318593\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | − | 22.0000i | −0.579721 | − | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.7975 | 1.69388 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7964 | 0.546519 | 0.273260 | − | 0.961940i | \(-0.411898\pi\) | ||||
0.273260 | + | 0.961940i | \(0.411898\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.67376 | + | 4.38197i | 0.0617376 | + | 0.161631i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.14333i | 0.152622i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 47.3071i | − | 1.74022i | −0.492858 | − | 0.870110i | \(-0.664048\pi\) | ||
0.492858 | − | 0.870110i | \(-0.335952\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.0506 | + | 44.6390i | 0.626369 | + | 1.63986i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.1083 | −1.25131 | −0.625657 | − | 0.780098i | \(-0.715169\pi\) | ||||
−0.625657 | + | 0.780098i | \(0.715169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.9793 | 0.658710 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.05192 | − | 4.51857i | 0.184840 | − | 0.165326i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.56239i | 0.203245i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.9771i | 1.38581i | 0.721031 | + | 0.692903i | \(0.243668\pi\) | ||||
−0.721031 | + | 0.692903i | \(0.756332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.1121 | + | 6.91822i | −0.660043 | + | 0.252114i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.9886 | −0.472702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.4628 | −0.416624 | −0.208312 | − | 0.978062i | \(-0.566797\pi\) | ||||
−0.208312 | + | 0.978062i | \(0.566797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8474 | + | 4.14333i | −0.393735 | + | 0.150393i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7.16573i | − | 0.259757i | −0.991530 | − | 0.129879i | \(-0.958541\pi\) | ||
0.991530 | − | 0.129879i | \(-0.0414588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 21.4940i | − | 0.778136i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.10452 | + | 8.14333i | −0.329175 | + | 0.294423i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.50499 | −0.126558 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.18449 | 0.331201 | 0.165601 | − | 0.986193i | \(-0.447044\pi\) | ||||
0.165601 | + | 0.986193i | \(0.447044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.01774 | − | 5.28251i | −0.0726670 | − | 0.190245i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.9121i | 1.14780i | 0.818926 | + | 0.573899i | \(0.194570\pi\) | ||||
−0.818926 | + | 0.573899i | \(0.805430\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.70405i | 0.312659i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.3059 | + | 32.2173i | 0.441473 | + | 1.15579i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.9114 | 0.928373 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.37940 | 0.192490 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1025 | − | 5.21084i | −0.361034 | − | 0.186220i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 21.6483i | − | 0.772662i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 32.9931i | − | 1.17608i | −0.808833 | − | 0.588038i | \(-0.799901\pi\) | ||
0.808833 | − | 0.588038i | \(-0.200099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.0720 | + | 7.28486i | −0.678982 | + | 0.259348i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.2153 | 1.00322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.63834 | 0.164712 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.61131 | − | 3.67119i | 0.340878 | − | 0.130204i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.8522i | 1.26995i | 0.772532 | + | 0.634975i | \(0.218990\pi\) | ||||
−0.772532 | + | 0.634975i | \(0.781010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 40.4728i | − | 1.43183i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.0100 | − | 39.1423i | −1.23702 | − | 1.38303i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.25929 | 0.150307 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.8885 | −0.489507 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.657612 | − | 1.72165i | −0.0231490 | − | 0.0606049i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 13.3319i | − | 0.468726i | −0.972149 | − | 0.234363i | \(-0.924700\pi\) | ||
0.972149 | − | 0.234363i | \(-0.0753004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.6681i | − | 0.725754i | −0.931837 | − | 0.362877i | \(-0.881795\pi\) | ||
0.931837 | − | 0.362877i | \(-0.118205\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.71882 | + | 12.3540i | 0.165496 | + | 0.433275i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.1017 | 1.64788 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.2966 | + | 30.5186i | 0.953822 | + | 1.06641i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1876i | 0.634752i | 0.948300 | + | 0.317376i | \(0.102802\pi\) | ||||
−0.948300 | + | 0.317376i | \(0.897198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.4638i | 0.573893i | 0.957947 | + | 0.286946i | \(0.0926402\pi\) | ||||
−0.957947 | + | 0.286946i | \(0.907360\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.61803 | + | 0.618034i | −0.0563327 | + | 0.0215172i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.6435 | 1.76105 | 0.880524 | − | 0.474001i | \(-0.157191\pi\) | ||||
0.880524 | + | 0.474001i | \(0.157191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9866 | −1.24986 | −0.624932 | − | 0.780679i | \(-0.714873\pi\) | ||||
−0.624932 | + | 0.780679i | \(0.714873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6833 | + | 10.1921i | −0.925634 | + | 0.353561i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 11.0269i | − | 0.382059i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 25.5324i | − | 0.883584i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.1956 | + | 20.7327i | 1.38936 | + | 0.716629i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4020 | −1.53293 | −0.766463 | − | 0.642288i | \(-0.777985\pi\) | ||||
−0.766463 | + | 0.642288i | \(0.777985\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.2143 | 0.834976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.7273 | + | 35.9385i | 0.472792 | + | 1.23779i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 30.4030i | − | 1.04589i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.07167i | 0.0711833i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.04747 | + | 15.8325i | 0.207548 | + | 0.543369i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.4347 | 2.20879 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.4136 | −1.04134 | −0.520671 | − | 0.853758i | \(-0.674318\pi\) | ||||
−0.520671 | + | 0.853758i | \(0.674318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.36381 | + | 8.37524i | −0.320235 | + | 0.286427i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 17.7976i | − | 0.607955i | −0.952679 | − | 0.303977i | \(-0.901685\pi\) | ||
0.952679 | − | 0.303977i | \(-0.0983147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 26.3102i | − | 0.897693i | −0.893609 | − | 0.448847i | \(-0.851835\pi\) | ||
0.893609 | − | 0.448847i | \(-0.148165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.7411 | − | 7.92238i | 0.706853 | − | 0.269994i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.6864 | −1.07862 | −0.539310 | − | 0.842108i | \(-0.681315\pi\) | ||||
−0.539310 | + | 0.842108i | \(0.681315\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5767 | 0.393618 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.682072 | + | 0.260528i | −0.0231644 | + | 0.00884801i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.9557i | 0.405570i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.2966i | − | 0.924911i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.5566 | − | 15.7031i | 0.594200 | − | 0.531468i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.07167 | −0.0700351 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.9259 | 1.78718 | 0.893590 | − | 0.448883i | \(-0.148178\pi\) | ||||
0.893590 | + | 0.448883i | \(0.148178\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.8359 | + | 30.9869i | 0.399216 | + | 1.04516i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 11.0412i | − | 0.371986i | −0.982551 | − | 0.185993i | \(-0.940450\pi\) | ||
0.982551 | − | 0.185993i | \(-0.0595502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.7739i | 0.732751i | 0.930467 | + | 0.366375i | \(0.119401\pi\) | ||||
−0.930467 | + | 0.366375i | \(0.880599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.328806 | − | 0.860825i | −0.0110527 | − | 0.0289363i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.71784 | 0.259140 | 0.129570 | − | 0.991570i | \(-0.458640\pi\) | ||||
0.129570 | + | 0.991570i | \(0.458640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.8651 | −0.699794 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 8.94427i | −0.0335013 | + | 0.299644i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 41.6254i | − | 1.39294i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.7917i | 0.461004i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 71.4635 | − | 27.2966i | 2.38610 | − | 0.911408i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.0412 | 0.635058 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.1862 | −0.805758 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.7031 | − | 14.4013i | 1.25468 | − | 0.479245i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9949i | 0.797616i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.2513i | 0.506412i | 0.967412 | + | 0.253206i | \(0.0814850\pi\) | ||||
−0.967412 | + | 0.253206i | \(0.918515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.1423 | − | 28.1100i | −0.833919 | − | 0.932350i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7442 | −0.819813 | −0.409907 | − | 0.912128i | \(-0.634439\pi\) | ||||
−0.409907 | + | 0.912128i | \(0.634439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.25929 | −0.0747715 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.435126 | + | 1.13918i | 0.0143848 | + | 0.0376600i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 5.41837i | − | 0.178930i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.0367i | − | 0.660949i | −0.943815 | − | 0.330474i | \(-0.892791\pi\) | ||
0.943815 | − | 0.330474i | \(-0.107209\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.47942 | − | 22.1994i | −0.279406 | − | 0.731495i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.4400 | −1.16652 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.61131 | 0.316018 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.8885 | − | 20.0000i | −0.587537 | − | 0.656886i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.2183i | 0.630533i | 0.949003 | + | 0.315266i | \(0.102094\pi\) | ||||
−0.949003 | + | 0.315266i | \(0.897906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 11.3409i | − | 0.371684i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.6113 | − | 8.25479i | 0.707523 | − | 0.270250i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.07167 | 0.133158 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.9083 | −1.63043 | −0.815217 | − | 0.579156i | \(-0.803382\pi\) | ||||
−0.815217 | + | 0.579156i | \(0.803382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.8381 | − | 9.10534i | 0.777927 | − | 0.297142i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.08644i | − | 0.133214i | −0.997779 | − | 0.0666070i | \(-0.978783\pi\) | ||
0.997779 | − | 0.0666070i | \(-0.0212174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 41.4821i | − | 1.35084i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.93464 | + | 9.56702i | −0.160524 | + | 0.311215i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.3091 | −0.529975 | −0.264987 | − | 0.964252i | \(-0.585368\pi\) | ||||
−0.264987 | + | 0.964252i | \(0.585368\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0606 | −0.910885 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.94525 | − | 5.09274i | −0.0630791 | − | 0.165143i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.6407i | − | 0.409472i | −0.978817 | − | 0.204736i | \(-0.934366\pi\) | ||
0.978817 | − | 0.204736i | \(-0.0656336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.560719i | 0.0181444i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.35202 | + | 3.53965i | 0.0437047 | + | 0.114421i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.2071 | 1.29835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.7605 | −1.44389 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00381 | − | 5.36997i | 0.193470 | − | 0.173045i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.26858i | 0.169602i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.7290i | 1.98507i | 0.121959 | + | 0.992535i | \(0.461082\pi\) | ||||
−0.121959 | + | 0.992535i | \(0.538918\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.5884 | − | 10.5378i | 0.886268 | − | 0.338524i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.9257 | −0.864087 | −0.432043 | − | 0.901853i | \(-0.642207\pi\) | ||||
−0.432043 | + | 0.901853i | \(0.642207\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6651 | 0.534258 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.6598 | − | 4.07167i | 0.341385 | − | 0.130398i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.0017i | 1.11980i | 0.828559 | + | 0.559901i | \(0.189161\pi\) | ||||
−0.828559 | + | 0.559901i | \(0.810839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5050i | 0.559462i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.1997 | + | 20.7505i | −0.740711 | + | 0.662512i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.6473 | 0.530968 | 0.265484 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265484 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.3355 | 0.711667 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7269 | − | 33.3195i | −0.405102 | − | 1.06057i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 75.4061i | − | 2.39778i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.5826i | 0.494998i | 0.968888 | + | 0.247499i | \(0.0796087\pi\) | ||||
−0.968888 | + | 0.247499i | \(0.920391\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.38038 | − | 11.4680i | −0.139007 | − | 0.363925i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.375243 | 0.0118960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.13219 | −0.162538 | −0.0812691 | − | 0.996692i | \(-0.525897\pi\) | ||||
−0.0812691 | + | 0.996692i | \(0.525897\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.8938 | − | 44.3854i | 0.724328 | − | 1.40429i |
(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 | 2640.2.k.c.1871.4 | yes | 8 | |
3.2 | odd | 2 | 2640.2.k.e.1871.8 | yes | 8 | ||
4.3 | odd | 2 | 2640.2.k.e.1871.5 | yes | 8 | ||
12.11 | even | 2 | inner | 2640.2.k.c.1871.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2640.2.k.c.1871.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
2640.2.k.c.1871.4 | yes | 8 | 1.1 | even | 1 | trivial | |
2640.2.k.e.1871.5 | yes | 8 | 4.3 | odd | 2 | ||
2640.2.k.e.1871.8 | yes | 8 | 3.2 | odd | 2 |