Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.a (trivial) |
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: | yes |
Analytic conductor: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.85410 | 1.27639 | 0.638197 | − | 0.769873i | \(-0.279681\pi\) | ||||
0.638197 | + | 0.769873i | \(0.279681\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.85410 | −0.902546 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 7.85410 | 1.90490 | 0.952450 | − | 0.304696i | \(-0.0985548\pi\) | ||||
0.952450 | + | 0.304696i | \(0.0985548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61803 | −0.600618 | −0.300309 | − | 0.953842i | \(-0.597090\pi\) | ||||
−0.300309 | + | 0.953842i | \(0.597090\pi\) | |||||||
\(20\) | −2.85410 | −0.638197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.09017 | 0.644345 | 0.322172 | − | 0.946681i | \(-0.395587\pi\) | ||||
0.322172 | + | 0.946681i | \(0.395587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.14590 | 0.629180 | ||||||||
\(26\) | −1.23607 | −0.242413 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.32624 | −1.31583 | −0.657916 | − | 0.753092i | \(-0.728562\pi\) | ||||
−0.657916 | + | 0.753092i | \(0.728562\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.85410 | −1.34697 | ||||||||
\(35\) | −2.85410 | −0.482431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12.0902 | −1.98761 | −0.993806 | − | 0.111130i | \(-0.964553\pi\) | ||||
−0.993806 | + | 0.111130i | \(0.964553\pi\) | |||||||
\(38\) | 2.61803 | 0.424701 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.56231 | 1.35382 | ||||||||
\(41\) | −10.8541 | −1.69513 | −0.847563 | − | 0.530695i | \(-0.821931\pi\) | ||||
−0.847563 | + | 0.530695i | \(0.821931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.23607 | 0.188499 | 0.0942493 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942493 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.09017 | −0.455621 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.14590 | −0.444897 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.23607 | −0.171412 | ||||||||
\(53\) | −12.1803 | −1.67310 | −0.836549 | − | 0.547892i | \(-0.815431\pi\) | ||||
−0.836549 | + | 0.547892i | \(0.815431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −6.76393 | −0.880589 | −0.440294 | − | 0.897853i | \(-0.645126\pi\) | ||||
−0.440294 | + | 0.897853i | \(0.645126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.94427 | −1.14520 | −0.572598 | − | 0.819836i | \(-0.694065\pi\) | ||||
−0.572598 | + | 0.819836i | \(0.694065\pi\) | |||||||
\(62\) | 7.32624 | 0.930433 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 3.52786 | 0.437578 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | −7.85410 | −0.952450 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.85410 | 0.341130 | ||||||||
\(71\) | −8.94427 | −1.06149 | −0.530745 | − | 0.847532i | \(-0.678088\pi\) | ||||
−0.530745 | + | 0.847532i | \(0.678088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.23607 | 0.612835 | 0.306418 | − | 0.951897i | \(-0.400870\pi\) | ||||
0.306418 | + | 0.951897i | \(0.400870\pi\) | |||||||
\(74\) | 12.0902 | 1.40545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.61803 | 0.300309 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | −2.85410 | −0.319098 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.8541 | 1.19864 | ||||||||
\(83\) | 2.94427 | 0.323176 | 0.161588 | − | 0.986858i | \(-0.448338\pi\) | ||||
0.161588 | + | 0.986858i | \(0.448338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.4164 | 2.43140 | ||||||||
\(86\) | −1.23607 | −0.133289 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.09017 | −0.115558 | −0.0577789 | − | 0.998329i | \(-0.518402\pi\) | ||||
−0.0577789 | + | 0.998329i | \(0.518402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | −3.09017 | −0.322172 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −7.47214 | −0.766625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52786 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.14590 | −0.314590 | ||||||||
\(101\) | −2.09017 | −0.207980 | −0.103990 | − | 0.994578i | \(-0.533161\pi\) | ||||
−0.103990 | + | 0.994578i | \(0.533161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3262 | −1.01747 | −0.508737 | − | 0.860922i | \(-0.669888\pi\) | ||||
−0.508737 | + | 0.860922i | \(0.669888\pi\) | |||||||
\(104\) | 3.70820 | 0.363619 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1803 | 1.18306 | ||||||||
\(107\) | 4.90983 | 0.474651 | 0.237326 | − | 0.971430i | \(-0.423729\pi\) | ||||
0.237326 | + | 0.971430i | \(0.423729\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5623 | −1.01169 | −0.505843 | − | 0.862626i | \(-0.668818\pi\) | ||||
−0.505843 | + | 0.862626i | \(0.668818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −0.763932 | −0.0718647 | −0.0359323 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359323 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.81966 | 0.822438 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.76393 | 0.622670 | ||||||||
\(119\) | −7.85410 | −0.719984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.94427 | 0.809776 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.32624 | 0.657916 | ||||||||
\(125\) | −5.29180 | −0.473313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.23607 | 0.287155 | 0.143577 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143577 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.52786 | −0.309414 | ||||||||
\(131\) | 2.29180 | 0.200235 | 0.100118 | − | 0.994976i | \(-0.468078\pi\) | ||||
0.100118 | + | 0.994976i | \(0.468078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.61803 | 0.227012 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 23.5623 | 2.02045 | ||||||||
\(137\) | −6.76393 | −0.577882 | −0.288941 | − | 0.957347i | \(-0.593303\pi\) | ||||
−0.288941 | + | 0.957347i | \(0.593303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.79837 | −0.406993 | −0.203496 | − | 0.979076i | \(-0.565231\pi\) | ||||
−0.203496 | + | 0.979076i | \(0.565231\pi\) | |||||||
\(140\) | 2.85410 | 0.241216 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.94427 | 0.750587 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.70820 | −0.474041 | ||||||||
\(146\) | −5.23607 | −0.433340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.0902 | 0.993806 | ||||||||
\(149\) | −20.0000 | −1.63846 | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | −7.85410 | −0.637052 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.9098 | −1.67952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.70820 | 0.774799 | 0.387400 | − | 0.921912i | \(-0.373373\pi\) | ||||
0.387400 | + | 0.921912i | \(0.373373\pi\) | |||||||
\(158\) | −14.0000 | −1.11378 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −14.2705 | −1.12818 | ||||||||
\(161\) | −3.09017 | −0.243540 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.41641 | −0.424246 | −0.212123 | − | 0.977243i | \(-0.568038\pi\) | ||||
−0.212123 | + | 0.977243i | \(0.568038\pi\) | |||||||
\(164\) | 10.8541 | 0.847563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.94427 | −0.228520 | ||||||||
\(167\) | 8.18034 | 0.633014 | 0.316507 | − | 0.948590i | \(-0.397490\pi\) | ||||
0.316507 | + | 0.948590i | \(0.397490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | −22.4164 | −1.71926 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.23607 | −0.0942493 | ||||||||
\(173\) | 19.8541 | 1.50948 | 0.754740 | − | 0.656024i | \(-0.227763\pi\) | ||||
0.754740 | + | 0.656024i | \(0.227763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.14590 | −0.237808 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.09017 | 0.0817117 | ||||||||
\(179\) | −8.38197 | −0.626498 | −0.313249 | − | 0.949671i | \(-0.601417\pi\) | ||||
−0.313249 | + | 0.949671i | \(0.601417\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.9443 | −1.40812 | −0.704058 | − | 0.710142i | \(-0.748631\pi\) | ||||
−0.704058 | + | 0.710142i | \(0.748631\pi\) | |||||||
\(182\) | 1.23607 | 0.0916235 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.27051 | 0.683431 | ||||||||
\(185\) | −34.5066 | −2.53697 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.47214 | 0.542086 | ||||||||
\(191\) | 18.2705 | 1.32201 | 0.661004 | − | 0.750383i | \(-0.270131\pi\) | ||||
0.661004 | + | 0.750383i | \(0.270131\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.3820 | −1.32316 | −0.661581 | − | 0.749873i | \(-0.730114\pi\) | ||||
−0.661581 | + | 0.749873i | \(0.730114\pi\) | |||||||
\(194\) | 3.52786 | 0.253286 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.61803 | −0.185588 | −0.0927938 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927938 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(200\) | 9.43769 | 0.667346 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.09017 | 0.147064 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.9787 | −2.16365 | ||||||||
\(206\) | 10.3262 | 0.719463 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.23607 | −0.0857059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 12.1803 | 0.836549 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.90983 | −0.335629 | ||||||||
\(215\) | 3.52786 | 0.240598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.32624 | 0.497337 | ||||||||
\(218\) | 10.5623 | 0.715370 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70820 | 0.653044 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7984 | 1.39276 | 0.696381 | − | 0.717672i | \(-0.254792\pi\) | ||||
0.696381 | + | 0.717672i | \(0.254792\pi\) | |||||||
\(224\) | 5.00000 | 0.334077 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.763932 | 0.0508160 | ||||||||
\(227\) | 21.4164 | 1.42146 | 0.710728 | − | 0.703466i | \(-0.248365\pi\) | ||||
0.710728 | + | 0.703466i | \(0.248365\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2361 | 1.40332 | 0.701659 | − | 0.712512i | \(-0.252443\pi\) | ||||
0.701659 | + | 0.712512i | \(0.252443\pi\) | |||||||
\(230\) | −8.81966 | −0.581551 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −5.70820 | −0.373957 | −0.186978 | − | 0.982364i | \(-0.559869\pi\) | ||||
−0.186978 | + | 0.982364i | \(0.559869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.70820 | −0.372362 | ||||||||
\(236\) | 6.76393 | 0.440294 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.85410 | 0.509106 | ||||||||
\(239\) | −1.56231 | −0.101057 | −0.0505286 | − | 0.998723i | \(-0.516091\pi\) | ||||
−0.0505286 | + | 0.998723i | \(0.516091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.94427 | −0.318489 | −0.159244 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159244 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.94427 | 0.572598 | ||||||||
\(245\) | 2.85410 | 0.182342 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.23607 | −0.205906 | ||||||||
\(248\) | −21.9787 | −1.39565 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.29180 | 0.334683 | ||||||||
\(251\) | −24.1803 | −1.52625 | −0.763125 | − | 0.646251i | \(-0.776336\pi\) | ||||
−0.763125 | + | 0.646251i | \(0.776336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.23607 | −0.203049 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | −2.61803 | −0.163308 | −0.0816542 | − | 0.996661i | \(-0.526020\pi\) | ||||
−0.0816542 | + | 0.996661i | \(0.526020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0902 | 0.751247 | ||||||||
\(260\) | −3.52786 | −0.218789 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.29180 | −0.141588 | ||||||||
\(263\) | 2.43769 | 0.150315 | 0.0751573 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751573 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.7639 | −2.13553 | ||||||||
\(266\) | −2.61803 | −0.160522 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | −27.8885 | −1.70039 | −0.850197 | − | 0.526464i | \(-0.823517\pi\) | ||||
−0.850197 | + | 0.526464i | \(0.823517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0902 | −1.46337 | −0.731687 | − | 0.681641i | \(-0.761267\pi\) | ||||
−0.731687 | + | 0.681641i | \(0.761267\pi\) | |||||||
\(272\) | −7.85410 | −0.476225 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.76393 | 0.408624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4377 | 0.627140 | 0.313570 | − | 0.949565i | \(-0.398475\pi\) | ||||
0.313570 | + | 0.949565i | \(0.398475\pi\) | |||||||
\(278\) | 4.79837 | 0.287787 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.56231 | −0.511696 | ||||||||
\(281\) | 1.05573 | 0.0629795 | 0.0314897 | − | 0.999504i | \(-0.489975\pi\) | ||||
0.0314897 | + | 0.999504i | \(0.489975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4377 | −0.798788 | −0.399394 | − | 0.916779i | \(-0.630779\pi\) | ||||
−0.399394 | + | 0.916779i | \(0.630779\pi\) | |||||||
\(284\) | 8.94427 | 0.530745 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.8541 | 0.640697 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.6869 | 2.62864 | ||||||||
\(290\) | 5.70820 | 0.335197 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.23607 | −0.306418 | ||||||||
\(293\) | 19.7984 | 1.15663 | 0.578317 | − | 0.815812i | \(-0.303710\pi\) | ||||
0.578317 | + | 0.815812i | \(0.303710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.3050 | −1.12398 | ||||||||
\(296\) | −36.2705 | −2.10818 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.0000 | 1.15857 | ||||||||
\(299\) | 3.81966 | 0.220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.23607 | −0.0712458 | ||||||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.61803 | 0.150155 | ||||||||
\(305\) | −25.5279 | −1.46172 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.2705 | 1.38519 | 0.692596 | − | 0.721326i | \(-0.256467\pi\) | ||||
0.692596 | + | 0.721326i | \(0.256467\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.9098 | 1.18760 | ||||||||
\(311\) | 0.763932 | 0.0433186 | 0.0216593 | − | 0.999765i | \(-0.493105\pi\) | ||||
0.0216593 | + | 0.999765i | \(0.493105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.81966 | −0.555040 | −0.277520 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277520 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(314\) | −9.70820 | −0.547866 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | 27.5967 | 1.54999 | 0.774994 | − | 0.631969i | \(-0.217753\pi\) | ||||
0.774994 | + | 0.631969i | \(0.217753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 19.9787 | 1.11684 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.09017 | 0.172208 | ||||||||
\(323\) | −20.5623 | −1.14412 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.88854 | 0.215698 | ||||||||
\(326\) | 5.41641 | 0.299987 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −32.5623 | −1.79795 | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.3607 | 1.66877 | 0.834387 | − | 0.551179i | \(-0.185822\pi\) | ||||
0.834387 | + | 0.551179i | \(0.185822\pi\) | |||||||
\(332\) | −2.94427 | −0.161588 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.18034 | −0.447608 | ||||||||
\(335\) | 22.8328 | 1.24749 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.1459 | 1.47873 | 0.739366 | − | 0.673304i | \(-0.235126\pi\) | ||||
0.739366 | + | 0.673304i | \(0.235126\pi\) | |||||||
\(338\) | 11.4721 | 0.624002 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.4164 | −1.21570 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.70820 | 0.199933 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.8541 | −1.06736 | ||||||||
\(347\) | −12.3820 | −0.664699 | −0.332349 | − | 0.943156i | \(-0.607841\pi\) | ||||
−0.332349 | + | 0.943156i | \(0.607841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7639 | −1.21853 | −0.609263 | − | 0.792968i | \(-0.708534\pi\) | ||||
−0.609263 | + | 0.792968i | \(0.708534\pi\) | |||||||
\(350\) | 3.14590 | 0.168155 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4721 | −0.663825 | −0.331912 | − | 0.943310i | \(-0.607694\pi\) | ||||
−0.331912 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.5279 | −1.35488 | ||||||||
\(356\) | 1.09017 | 0.0577789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.38197 | 0.443001 | ||||||||
\(359\) | 7.03444 | 0.371264 | 0.185632 | − | 0.982619i | \(-0.440567\pi\) | ||||
0.185632 | + | 0.982619i | \(0.440567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1459 | −0.639258 | ||||||||
\(362\) | 18.9443 | 0.995689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.23607 | 0.0647876 | ||||||||
\(365\) | 14.9443 | 0.782219 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2705 | 0.849314 | 0.424657 | − | 0.905354i | \(-0.360395\pi\) | ||||
0.424657 | + | 0.905354i | \(0.360395\pi\) | |||||||
\(368\) | −3.09017 | −0.161086 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.5066 | 1.79391 | ||||||||
\(371\) | 12.1803 | 0.632372 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3262 | 1.20779 | 0.603893 | − | 0.797065i | \(-0.293615\pi\) | ||||
0.603893 | + | 0.797065i | \(0.293615\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | −2.47214 | −0.127321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.47214 | 0.126985 | 0.0634925 | − | 0.997982i | \(-0.479776\pi\) | ||||
0.0634925 | + | 0.997982i | \(0.479776\pi\) | |||||||
\(380\) | 7.47214 | 0.383312 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.2705 | −0.934801 | ||||||||
\(383\) | 13.0557 | 0.667117 | 0.333558 | − | 0.942729i | \(-0.391751\pi\) | ||||
0.333558 | + | 0.942729i | \(0.391751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.3820 | 0.935617 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.52786 | 0.179100 | ||||||||
\(389\) | −22.1803 | −1.12459 | −0.562294 | − | 0.826937i | \(-0.690081\pi\) | ||||
−0.562294 | + | 0.826937i | \(0.690081\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.2705 | 1.22741 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | 39.9574 | 2.01048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6525 | 0.735387 | 0.367693 | − | 0.929947i | \(-0.380148\pi\) | ||||
0.367693 | + | 0.929947i | \(0.380148\pi\) | |||||||
\(398\) | 2.61803 | 0.131230 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.14590 | −0.157295 | ||||||||
\(401\) | −18.4721 | −0.922454 | −0.461227 | − | 0.887282i | \(-0.652591\pi\) | ||||
−0.461227 | + | 0.887282i | \(0.652591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.05573 | −0.451098 | ||||||||
\(404\) | 2.09017 | 0.103990 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.00000 | −0.0992583 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.7639 | −1.42228 | −0.711142 | − | 0.703048i | \(-0.751822\pi\) | ||||
−0.711142 | + | 0.703048i | \(0.751822\pi\) | |||||||
\(410\) | 30.9787 | 1.52993 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.3262 | 0.508737 | ||||||||
\(413\) | 6.76393 | 0.332831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.40325 | 0.412499 | ||||||||
\(416\) | −6.18034 | −0.303016 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.7639 | −0.721265 | −0.360633 | − | 0.932708i | \(-0.617439\pi\) | ||||
−0.360633 | + | 0.932708i | \(0.617439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.32624 | −0.210848 | −0.105424 | − | 0.994427i | \(-0.533620\pi\) | ||||
−0.105424 | + | 0.994427i | \(0.533620\pi\) | |||||||
\(422\) | −2.00000 | −0.0973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −36.5410 | −1.77459 | ||||||||
\(425\) | 24.7082 | 1.19852 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.94427 | 0.432844 | ||||||||
\(428\) | −4.90983 | −0.237326 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.52786 | −0.170129 | ||||||||
\(431\) | −2.09017 | −0.100680 | −0.0503400 | − | 0.998732i | \(-0.516030\pi\) | ||||
−0.0503400 | + | 0.998732i | \(0.516030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2361 | −0.828313 | −0.414156 | − | 0.910206i | \(-0.635923\pi\) | ||||
−0.414156 | + | 0.910206i | \(0.635923\pi\) | |||||||
\(434\) | −7.32624 | −0.351671 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.5623 | 0.505843 | ||||||||
\(437\) | −8.09017 | −0.387005 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7984 | 1.04038 | 0.520190 | − | 0.854051i | \(-0.325861\pi\) | ||||
0.520190 | + | 0.854051i | \(0.325861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.70820 | −0.461772 | ||||||||
\(443\) | −4.90983 | −0.233273 | −0.116637 | − | 0.993175i | \(-0.537211\pi\) | ||||
−0.116637 | + | 0.993175i | \(0.537211\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.11146 | −0.147497 | ||||||||
\(446\) | −20.7984 | −0.984832 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.00000 | −0.330719 | ||||||||
\(449\) | −41.8885 | −1.97684 | −0.988421 | − | 0.151734i | \(-0.951514\pi\) | ||||
−0.988421 | + | 0.151734i | \(0.951514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.763932 | 0.0359323 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.4164 | −1.00512 | ||||||||
\(455\) | −3.52786 | −0.165389 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.4721 | −0.583422 | −0.291711 | − | 0.956507i | \(-0.594225\pi\) | ||||
−0.291711 | + | 0.956507i | \(0.594225\pi\) | |||||||
\(458\) | −21.2361 | −0.992296 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.81966 | −0.411219 | ||||||||
\(461\) | −6.36068 | −0.296246 | −0.148123 | − | 0.988969i | \(-0.547323\pi\) | ||||
−0.148123 | + | 0.988969i | \(0.547323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4164 | 0.530565 | 0.265283 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265283 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.70820 | 0.264427 | ||||||||
\(467\) | −19.2361 | −0.890139 | −0.445070 | − | 0.895496i | \(-0.646821\pi\) | ||||
−0.445070 | + | 0.895496i | \(0.646821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | 5.70820 | 0.263300 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.2918 | −0.934006 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.23607 | −0.377897 | ||||||||
\(476\) | 7.85410 | 0.359992 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.56231 | 0.0714582 | ||||||||
\(479\) | −11.0557 | −0.505149 | −0.252575 | − | 0.967577i | \(-0.581277\pi\) | ||||
−0.252575 | + | 0.967577i | \(0.581277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.9443 | −0.681400 | ||||||||
\(482\) | 4.94427 | 0.225205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0689 | −0.457204 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.2361 | −1.77796 | −0.888978 | − | 0.457950i | \(-0.848584\pi\) | ||||
−0.888978 | + | 0.457950i | \(0.848584\pi\) | |||||||
\(488\) | −26.8328 | −1.21466 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.85410 | −0.128935 | ||||||||
\(491\) | −0.326238 | −0.0147229 | −0.00736146 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736146 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7082 | −0.707462 | ||||||||
\(494\) | 3.23607 | 0.145598 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.32624 | 0.328958 | ||||||||
\(497\) | 8.94427 | 0.401205 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1803 | 1.17199 | 0.585996 | − | 0.810314i | \(-0.300703\pi\) | ||||
0.585996 | + | 0.810314i | \(0.300703\pi\) | |||||||
\(500\) | 5.29180 | 0.236656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.1803 | 1.07922 | ||||||||
\(503\) | −0.583592 | −0.0260211 | −0.0130105 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130105 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.96556 | −0.265464 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.23607 | −0.143577 | ||||||||
\(509\) | 5.90983 | 0.261949 | 0.130974 | − | 0.991386i | \(-0.458189\pi\) | ||||
0.130974 | + | 0.991386i | \(0.458189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.23607 | −0.231630 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.61803 | 0.115477 | ||||||||
\(515\) | −29.4721 | −1.29870 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −12.0902 | −0.531212 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.5836 | 0.464121 | ||||||||
\(521\) | 11.6180 | 0.508995 | 0.254498 | − | 0.967073i | \(-0.418090\pi\) | ||||
0.254498 | + | 0.967073i | \(0.418090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.90983 | −0.127238 | −0.0636190 | − | 0.997974i | \(-0.520264\pi\) | ||||
−0.0636190 | + | 0.997974i | \(0.520264\pi\) | |||||||
\(524\) | −2.29180 | −0.100118 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.43769 | −0.106289 | ||||||||
\(527\) | −57.5410 | −2.50653 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.4508 | −0.584820 | ||||||||
\(530\) | 34.7639 | 1.51005 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.61803 | −0.113506 | ||||||||
\(533\) | −13.4164 | −0.581129 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0132 | 0.605842 | ||||||||
\(536\) | 24.0000 | 1.03664 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.8885 | 1.20236 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8541 | −0.724614 | −0.362307 | − | 0.932059i | \(-0.618011\pi\) | ||||
−0.362307 | + | 0.932059i | \(0.618011\pi\) | |||||||
\(542\) | 24.0902 | 1.03476 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −39.2705 | −1.68371 | ||||||||
\(545\) | −30.1459 | −1.29131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.4721 | 1.55944 | 0.779718 | − | 0.626131i | \(-0.215362\pi\) | ||||
0.779718 | + | 0.626131i | \(0.215362\pi\) | |||||||
\(548\) | 6.76393 | 0.288941 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.23607 | 0.223064 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0000 | −0.595341 | ||||||||
\(554\) | −10.4377 | −0.443455 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.79837 | 0.203496 | ||||||||
\(557\) | −21.4164 | −0.907442 | −0.453721 | − | 0.891144i | \(-0.649904\pi\) | ||||
−0.453721 | + | 0.891144i | \(0.649904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.52786 | 0.0646218 | ||||||||
\(560\) | 2.85410 | 0.120608 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.05573 | −0.0445332 | ||||||||
\(563\) | 40.3607 | 1.70100 | 0.850500 | − | 0.525975i | \(-0.176300\pi\) | ||||
0.850500 | + | 0.525975i | \(0.176300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.18034 | −0.0917276 | ||||||||
\(566\) | 13.4377 | 0.564828 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −26.8328 | −1.12588 | ||||||||
\(569\) | −18.1803 | −0.762159 | −0.381080 | − | 0.924542i | \(-0.624448\pi\) | ||||
−0.381080 | + | 0.924542i | \(0.624448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5410 | −1.19440 | −0.597202 | − | 0.802091i | \(-0.703721\pi\) | ||||
−0.597202 | + | 0.802091i | \(0.703721\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.8541 | −0.453041 | ||||||||
\(575\) | 9.72136 | 0.405409 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6525 | −0.609991 | −0.304995 | − | 0.952354i | \(-0.598655\pi\) | ||||
−0.304995 | + | 0.952354i | \(0.598655\pi\) | |||||||
\(578\) | −44.6869 | −1.85873 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.70820 | 0.237020 | ||||||||
\(581\) | −2.94427 | −0.122149 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.7082 | 0.650010 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.7984 | −0.817863 | ||||||||
\(587\) | −3.88854 | −0.160497 | −0.0802487 | − | 0.996775i | \(-0.525571\pi\) | ||||
−0.0802487 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.1803 | 0.790312 | ||||||||
\(590\) | 19.3050 | 0.794772 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.0902 | 0.496903 | ||||||||
\(593\) | 3.43769 | 0.141169 | 0.0705846 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705846 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.4164 | −0.918983 | ||||||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.81966 | −0.156198 | ||||||||
\(599\) | 1.56231 | 0.0638341 | 0.0319170 | − | 0.999491i | \(-0.489839\pi\) | ||||
0.0319170 | + | 0.999491i | \(0.489839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 1.23607 | 0.0503784 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3262 | 0.419129 | 0.209565 | − | 0.977795i | \(-0.432795\pi\) | ||||
0.209565 | + | 0.977795i | \(0.432795\pi\) | |||||||
\(608\) | 13.0902 | 0.530876 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5279 | 1.03359 | ||||||||
\(611\) | −2.47214 | −0.100012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.85410 | 0.236445 | 0.118222 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118222 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(614\) | −24.2705 | −0.979478 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −44.6525 | −1.79764 | −0.898820 | − | 0.438317i | \(-0.855575\pi\) | ||||
−0.898820 | + | 0.438317i | \(0.855575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.5066 | −0.462488 | −0.231244 | − | 0.972896i | \(-0.574280\pi\) | ||||
−0.231244 | + | 0.972896i | \(0.574280\pi\) | |||||||
\(620\) | 20.9098 | 0.839759 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.763932 | −0.0306309 | ||||||||
\(623\) | 1.09017 | 0.0436767 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 9.81966 | 0.392473 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.70820 | −0.387400 | ||||||||
\(629\) | −94.9574 | −3.78620 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.8885 | 1.18984 | 0.594922 | − | 0.803783i | \(-0.297183\pi\) | ||||
0.594922 | + | 0.803783i | \(0.297183\pi\) | |||||||
\(632\) | 42.0000 | 1.67067 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.5967 | −1.09601 | ||||||||
\(635\) | 9.23607 | 0.366522 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.56231 | 0.338455 | ||||||||
\(641\) | −8.65248 | −0.341752 | −0.170876 | − | 0.985293i | \(-0.554660\pi\) | ||||
−0.170876 | + | 0.985293i | \(0.554660\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.9230 | 1.88990 | 0.944949 | − | 0.327218i | \(-0.106111\pi\) | ||||
0.944949 | + | 0.327218i | \(0.106111\pi\) | |||||||
\(644\) | 3.09017 | 0.121770 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.5623 | 0.809013 | ||||||||
\(647\) | 30.3607 | 1.19360 | 0.596801 | − | 0.802389i | \(-0.296438\pi\) | ||||
0.596801 | + | 0.802389i | \(0.296438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.88854 | −0.152521 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.41641 | 0.212123 | ||||||||
\(653\) | 25.8885 | 1.01310 | 0.506549 | − | 0.862211i | \(-0.330921\pi\) | ||||
0.506549 | + | 0.862211i | \(0.330921\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.54102 | 0.255579 | ||||||||
\(656\) | 10.8541 | 0.423781 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | −35.0344 | −1.36475 | −0.682374 | − | 0.731003i | \(-0.739052\pi\) | ||||
−0.682374 | + | 0.731003i | \(0.739052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.29180 | 0.322513 | 0.161257 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161257 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(662\) | −30.3607 | −1.18000 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.83282 | 0.342780 | ||||||||
\(665\) | 7.47214 | 0.289757 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.18034 | −0.239304 | ||||||||
\(668\) | −8.18034 | −0.316507 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.8328 | −0.882109 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.8885 | −1.38340 | −0.691701 | − | 0.722184i | \(-0.743138\pi\) | ||||
−0.691701 | + | 0.722184i | \(0.743138\pi\) | |||||||
\(674\) | −27.1459 | −1.04562 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.4721 | 0.441236 | ||||||||
\(677\) | 23.8885 | 0.918111 | 0.459056 | − | 0.888408i | \(-0.348188\pi\) | ||||
0.459056 | + | 0.888408i | \(0.348188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52786 | 0.135387 | ||||||||
\(680\) | 67.2492 | 2.57889 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.9230 | −1.56587 | −0.782937 | − | 0.622101i | \(-0.786279\pi\) | ||||
−0.782937 | + | 0.622101i | \(0.786279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.3050 | −0.737604 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.23607 | −0.0471246 | ||||||||
\(689\) | −15.0557 | −0.573578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.9230 | 1.51874 | 0.759371 | − | 0.650658i | \(-0.225507\pi\) | ||||
0.759371 | + | 0.650658i | \(0.225507\pi\) | |||||||
\(692\) | −19.8541 | −0.754740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.3820 | 0.470013 | ||||||||
\(695\) | −13.6950 | −0.519483 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −85.2492 | −3.22904 | ||||||||
\(698\) | 22.7639 | 0.861628 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.14590 | 0.118904 | ||||||||
\(701\) | 24.0689 | 0.909069 | 0.454535 | − | 0.890729i | \(-0.349806\pi\) | ||||
0.454535 | + | 0.890729i | \(0.349806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.6525 | 1.19380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.4721 | 0.469395 | ||||||||
\(707\) | 2.09017 | 0.0786089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.6869 | −0.739358 | −0.369679 | − | 0.929160i | \(-0.620532\pi\) | ||||
−0.369679 | + | 0.929160i | \(0.620532\pi\) | |||||||
\(710\) | 25.5279 | 0.958044 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.27051 | −0.122568 | ||||||||
\(713\) | −22.6393 | −0.847849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.38197 | 0.313249 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.03444 | −0.262523 | ||||||||
\(719\) | −4.87539 | −0.181821 | −0.0909106 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909106 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3262 | 0.384569 | ||||||||
\(722\) | 12.1459 | 0.452024 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.9443 | 0.704058 | ||||||||
\(725\) | −6.29180 | −0.233671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7426 | 0.954742 | 0.477371 | − | 0.878702i | \(-0.341590\pi\) | ||||
0.477371 | + | 0.878702i | \(0.341590\pi\) | |||||||
\(728\) | −3.70820 | −0.137435 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.9443 | −0.553112 | ||||||||
\(731\) | 9.70820 | 0.359071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.1246 | −1.14961 | −0.574807 | − | 0.818289i | \(-0.694923\pi\) | ||||
−0.574807 | + | 0.818289i | \(0.694923\pi\) | |||||||
\(734\) | −16.2705 | −0.600555 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.4508 | −0.569526 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.0132 | −1.80298 | −0.901489 | − | 0.432802i | \(-0.857525\pi\) | ||||
−0.901489 | + | 0.432802i | \(0.857525\pi\) | |||||||
\(740\) | 34.5066 | 1.26849 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.1803 | −0.447154 | ||||||||
\(743\) | 17.3262 | 0.635638 | 0.317819 | − | 0.948151i | \(-0.397050\pi\) | ||||
0.317819 | + | 0.948151i | \(0.397050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.0820 | −2.09132 | ||||||||
\(746\) | −23.3262 | −0.854034 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.90983 | −0.179401 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4721 | −0.382134 | −0.191067 | − | 0.981577i | \(-0.561195\pi\) | ||||
−0.191067 | + | 0.981577i | \(0.561195\pi\) | |||||||
\(752\) | 2.00000 | 0.0729325 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.47214 | 0.0900299 | ||||||||
\(755\) | 5.70820 | 0.207743 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.326238 | 0.0118573 | 0.00592866 | − | 0.999982i | \(-0.498113\pi\) | ||||
0.00592866 | + | 0.999982i | \(0.498113\pi\) | |||||||
\(758\) | −2.47214 | −0.0897920 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.4164 | −0.813129 | ||||||||
\(761\) | 45.7771 | 1.65942 | 0.829709 | − | 0.558196i | \(-0.188506\pi\) | ||||
0.829709 | + | 0.558196i | \(0.188506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.5623 | 0.382381 | ||||||||
\(764\) | −18.2705 | −0.661004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.0557 | −0.471723 | ||||||||
\(767\) | −8.36068 | −0.301887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5836 | −0.525898 | −0.262949 | − | 0.964810i | \(-0.584695\pi\) | ||||
−0.262949 | + | 0.964810i | \(0.584695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.3820 | 0.661581 | ||||||||
\(773\) | 38.9443 | 1.40073 | 0.700364 | − | 0.713786i | \(-0.253021\pi\) | ||||
0.700364 | + | 0.713786i | \(0.253021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.0476 | −0.827894 | ||||||||
\(776\) | −10.5836 | −0.379929 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.1803 | 0.795204 | ||||||||
\(779\) | 28.4164 | 1.01812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −24.2705 | −0.867912 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 27.7082 | 0.988948 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2705 | −0.437396 | −0.218698 | − | 0.975793i | \(-0.570181\pi\) | ||||
−0.218698 | + | 0.975793i | \(0.570181\pi\) | |||||||
\(788\) | −4.00000 | −0.142494 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −39.9574 | −1.42162 | ||||||||
\(791\) | 0.763932 | 0.0271623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0557 | −0.392600 | ||||||||
\(794\) | −14.6525 | −0.519997 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.61803 | 0.0927938 | ||||||||
\(797\) | −10.2705 | −0.363800 | −0.181900 | − | 0.983317i | \(-0.558225\pi\) | ||||
−0.181900 | + | 0.983317i | \(0.558225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7082 | −0.555716 | ||||||||
\(800\) | −15.7295 | −0.556121 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.4721 | 0.652274 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.81966 | −0.310852 | ||||||||
\(806\) | 9.05573 | 0.318974 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.27051 | −0.220596 | ||||||||
\(809\) | −28.6525 | −1.00737 | −0.503684 | − | 0.863888i | \(-0.668022\pi\) | ||||
−0.503684 | + | 0.863888i | \(0.668022\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3607 | 0.574501 | 0.287251 | − | 0.957855i | \(-0.407259\pi\) | ||||
0.287251 | + | 0.957855i | \(0.407259\pi\) | |||||||
\(812\) | −2.00000 | −0.0701862 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4590 | −0.541504 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.23607 | −0.113216 | ||||||||
\(818\) | 28.7639 | 1.00571 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.9787 | 1.08182 | ||||||||
\(821\) | 30.3607 | 1.05960 | 0.529798 | − | 0.848124i | \(-0.322268\pi\) | ||||
0.529798 | + | 0.848124i | \(0.322268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4721 | 0.853045 | 0.426523 | − | 0.904477i | \(-0.359738\pi\) | ||||
0.426523 | + | 0.904477i | \(0.359738\pi\) | |||||||
\(824\) | −30.9787 | −1.07919 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.76393 | −0.235347 | ||||||||
\(827\) | −4.32624 | −0.150438 | −0.0752190 | − | 0.997167i | \(-0.523966\pi\) | ||||
−0.0752190 | + | 0.997167i | \(0.523966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.9443 | 1.00528 | 0.502638 | − | 0.864497i | \(-0.332363\pi\) | ||||
0.502638 | + | 0.864497i | \(0.332363\pi\) | |||||||
\(830\) | −8.40325 | −0.291681 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.65248 | 0.299971 | ||||||||
\(833\) | 7.85410 | 0.272129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.3475 | 0.807974 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.7639 | 0.510012 | ||||||||
\(839\) | −33.4164 | −1.15366 | −0.576831 | − | 0.816863i | \(-0.695711\pi\) | ||||
−0.576831 | + | 0.816863i | \(0.695711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 4.32624 | 0.149092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.00000 | −0.0688428 | ||||||||
\(845\) | −32.7426 | −1.12638 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.1803 | 0.418275 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −24.7082 | −0.847484 | ||||||||
\(851\) | −37.3607 | −1.28071 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.7082 | 0.537839 | 0.268919 | − | 0.963163i | \(-0.413333\pi\) | ||||
0.268919 | + | 0.963163i | \(0.413333\pi\) | |||||||
\(854\) | −8.94427 | −0.306067 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.7295 | 0.503444 | ||||||||
\(857\) | −18.9443 | −0.647124 | −0.323562 | − | 0.946207i | \(-0.604880\pi\) | ||||
−0.323562 | + | 0.946207i | \(0.604880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.88854 | −0.200915 | −0.100457 | − | 0.994941i | \(-0.532031\pi\) | ||||
−0.100457 | + | 0.994941i | \(0.532031\pi\) | |||||||
\(860\) | −3.52786 | −0.120299 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.09017 | 0.0711915 | ||||||||
\(863\) | −37.6869 | −1.28288 | −0.641439 | − | 0.767174i | \(-0.721662\pi\) | ||||
−0.641439 | + | 0.767174i | \(0.721662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.6656 | 1.92669 | ||||||||
\(866\) | 17.2361 | 0.585705 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.32624 | −0.248669 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.88854 | 0.335061 | ||||||||
\(872\) | −31.6869 | −1.07305 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.09017 | 0.273654 | ||||||||
\(875\) | 5.29180 | 0.178895 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3607 | 1.56549 | 0.782744 | − | 0.622343i | \(-0.213819\pi\) | ||||
0.782744 | + | 0.622343i | \(0.213819\pi\) | |||||||
\(878\) | −21.7984 | −0.735659 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.4508 | 1.12699 | 0.563494 | − | 0.826120i | \(-0.309457\pi\) | ||||
0.563494 | + | 0.826120i | \(0.309457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.70820 | 0.259402 | 0.129701 | − | 0.991553i | \(-0.458598\pi\) | ||||
0.129701 | + | 0.991553i | \(0.458598\pi\) | |||||||
\(884\) | −9.70820 | −0.326522 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.90983 | 0.164949 | ||||||||
\(887\) | −46.5410 | −1.56269 | −0.781347 | − | 0.624097i | \(-0.785467\pi\) | ||||
−0.781347 | + | 0.624097i | \(0.785467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.23607 | −0.108534 | ||||||||
\(890\) | 3.11146 | 0.104296 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.7984 | −0.696381 | ||||||||
\(893\) | 5.23607 | 0.175218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.9230 | −0.799657 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.8885 | 1.39784 | ||||||||
\(899\) | 14.6525 | 0.488687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −95.6656 | −3.18708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.29180 | −0.0762240 | ||||||||
\(905\) | −54.0689 | −1.79731 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2361 | −1.56845 | −0.784224 | − | 0.620478i | \(-0.786939\pi\) | ||||
−0.784224 | + | 0.620478i | \(0.786939\pi\) | |||||||
\(908\) | −21.4164 | −0.710728 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.52786 | 0.116948 | ||||||||
\(911\) | 11.0557 | 0.366293 | 0.183146 | − | 0.983086i | \(-0.441372\pi\) | ||||
0.183146 | + | 0.983086i | \(0.441372\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 12.4721 | 0.412542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.2361 | −0.701659 | ||||||||
\(917\) | −2.29180 | −0.0756818 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.41641 | −0.244645 | −0.122322 | − | 0.992490i | \(-0.539034\pi\) | ||||
−0.122322 | + | 0.992490i | \(0.539034\pi\) | |||||||
\(920\) | 26.4590 | 0.872327 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.36068 | 0.209478 | ||||||||
\(923\) | −11.0557 | −0.363904 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.0344 | −1.25056 | ||||||||
\(926\) | −11.4164 | −0.375166 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.0000 | 0.328266 | ||||||||
\(929\) | 28.7984 | 0.944844 | 0.472422 | − | 0.881372i | \(-0.343380\pi\) | ||||
0.472422 | + | 0.881372i | \(0.343380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.61803 | −0.0858026 | ||||||||
\(932\) | 5.70820 | 0.186978 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.2361 | 0.629423 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7082 | −0.382490 | −0.191245 | − | 0.981542i | \(-0.561253\pi\) | ||||
−0.191245 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(938\) | 8.00000 | 0.261209 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.70820 | 0.186181 | ||||||||
\(941\) | −11.8541 | −0.386433 | −0.193216 | − | 0.981156i | \(-0.561892\pi\) | ||||
−0.193216 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.5410 | −1.09225 | ||||||||
\(944\) | 6.76393 | 0.220147 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.4377 | 0.761623 | 0.380811 | − | 0.924653i | \(-0.375645\pi\) | ||||
0.380811 | + | 0.924653i | \(0.375645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47214 | 0.210094 | ||||||||
\(950\) | 8.23607 | 0.267213 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.5623 | −0.763659 | ||||||||
\(953\) | 4.83282 | 0.156550 | 0.0782751 | − | 0.996932i | \(-0.475059\pi\) | ||||
0.0782751 | + | 0.996932i | \(0.475059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.1459 | 1.68740 | ||||||||
\(956\) | 1.56231 | 0.0505286 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.0557 | 0.357194 | ||||||||
\(959\) | 6.76393 | 0.218419 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6738 | 0.731412 | ||||||||
\(962\) | 14.9443 | 0.481823 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.94427 | 0.159244 | ||||||||
\(965\) | −52.4640 | −1.68888 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.3050 | −1.58554 | −0.792770 | − | 0.609521i | \(-0.791362\pi\) | ||||
−0.792770 | + | 0.609521i | \(0.791362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0689 | 0.323292 | ||||||||
\(971\) | −42.0689 | −1.35005 | −0.675027 | − | 0.737793i | \(-0.735868\pi\) | ||||
−0.675027 | + | 0.737793i | \(0.735868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.79837 | 0.153829 | ||||||||
\(974\) | 39.2361 | 1.25720 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.94427 | 0.286299 | ||||||||
\(977\) | 26.5836 | 0.850484 | 0.425242 | − | 0.905080i | \(-0.360189\pi\) | ||||
0.425242 | + | 0.905080i | \(0.360189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.85410 | −0.0911709 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.326238 | 0.0104107 | ||||||||
\(983\) | −48.4721 | −1.54602 | −0.773011 | − | 0.634393i | \(-0.781250\pi\) | ||||
−0.773011 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.4164 | 0.363757 | ||||||||
\(986\) | 15.7082 | 0.500251 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.23607 | 0.102953 | ||||||||
\(989\) | 3.81966 | 0.121458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.6525 | 0.592515 | 0.296258 | − | 0.955108i | \(-0.404261\pi\) | ||||
0.296258 | + | 0.955108i | \(0.404261\pi\) | |||||||
\(992\) | 36.6312 | 1.16304 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.94427 | −0.283695 | ||||||||
\(995\) | −7.47214 | −0.236883 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.5410 | 1.66399 | 0.831995 | − | 0.554783i | \(-0.187199\pi\) | ||||
0.831995 | + | 0.554783i | \(0.187199\pi\) | |||||||
\(998\) | −26.1803 | −0.828724 | ||||||||
\(999\) | 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 | 7623.2.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 2541.2.a.bd.1.1 | 2 | |||
11.2 | odd | 10 | 693.2.m.c.631.1 | 4 | |||
11.6 | odd | 10 | 693.2.m.c.190.1 | 4 | |||
11.10 | odd | 2 | 7623.2.a.bu.1.2 | 2 | |||
33.2 | even | 10 | 231.2.j.c.169.1 | ✓ | 4 | ||
33.17 | even | 10 | 231.2.j.c.190.1 | yes | 4 | ||
33.32 | even | 2 | 2541.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.c.169.1 | ✓ | 4 | 33.2 | even | 10 | ||
231.2.j.c.190.1 | yes | 4 | 33.17 | even | 10 | ||
693.2.m.c.190.1 | 4 | 11.6 | odd | 10 | |||
693.2.m.c.631.1 | 4 | 11.2 | odd | 10 | |||
2541.2.a.n.1.1 | 2 | 33.32 | even | 2 | |||
2541.2.a.bd.1.1 | 2 | 3.2 | odd | 2 | |||
7623.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7623.2.a.bu.1.2 | 2 | 11.10 | odd | 2 |