Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(1,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, 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("819.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.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: | \(6.53974792554\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.470683 | −0.332823 | −0.166412 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77846 | −0.889229 | ||||||||
\(5\) | −0.529317 | −0.236718 | −0.118359 | − | 0.992971i | \(-0.537763\pi\) | ||||
−0.118359 | + | 0.992971i | \(0.537763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.77846 | 0.628780 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.249141 | 0.0787852 | ||||||||
\(11\) | 2.24914 | 0.678141 | 0.339071 | − | 0.940761i | \(-0.389887\pi\) | ||||
0.339071 | + | 0.940761i | \(0.389887\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.470683 | 0.125795 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.71982 | 0.679956 | ||||||||
\(17\) | 1.30777 | 0.317182 | 0.158591 | − | 0.987344i | \(-0.449305\pi\) | ||||
0.158591 | + | 0.987344i | \(0.449305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.47068 | −0.337398 | −0.168699 | − | 0.985668i | \(-0.553957\pi\) | ||||
−0.168699 | + | 0.985668i | \(0.553957\pi\) | |||||||
\(20\) | 0.941367 | 0.210496 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.05863 | −0.225701 | ||||||||
\(23\) | −5.83709 | −1.21712 | −0.608559 | − | 0.793509i | \(-0.708252\pi\) | ||||
−0.608559 | + | 0.793509i | \(0.708252\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71982 | −0.943965 | ||||||||
\(26\) | −0.470683 | −0.0923086 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.77846 | 0.336097 | ||||||||
\(29\) | −5.22154 | −0.969616 | −0.484808 | − | 0.874621i | \(-0.661111\pi\) | ||||
−0.484808 | + | 0.874621i | \(0.661111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.02760 | −1.26219 | −0.631097 | − | 0.775704i | \(-0.717395\pi\) | ||||
−0.631097 | + | 0.775704i | \(0.717395\pi\) | |||||||
\(32\) | −4.83709 | −0.855085 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.615547 | −0.105566 | ||||||||
\(35\) | 0.529317 | 0.0894708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.36641 | −0.389035 | −0.194517 | − | 0.980899i | \(-0.562314\pi\) | ||||
−0.194517 | + | 0.980899i | \(0.562314\pi\) | |||||||
\(38\) | 0.692226 | 0.112294 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.941367 | −0.148843 | ||||||||
\(41\) | −6.49828 | −1.01486 | −0.507431 | − | 0.861693i | \(-0.669405\pi\) | ||||
−0.507431 | + | 0.861693i | \(0.669405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3940 | 1.73757 | 0.868785 | − | 0.495190i | \(-0.164902\pi\) | ||||
0.868785 | + | 0.495190i | \(0.164902\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.74742 | 0.405085 | ||||||||
\(47\) | −8.58451 | −1.25218 | −0.626090 | − | 0.779751i | \(-0.715346\pi\) | ||||
−0.626090 | + | 0.779751i | \(0.715346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.22154 | 0.314174 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.77846 | −0.246628 | ||||||||
\(53\) | −11.2767 | −1.54898 | −0.774490 | − | 0.632587i | \(-0.781993\pi\) | ||||
−0.774490 | + | 0.632587i | \(0.781993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.19051 | −0.160528 | ||||||||
\(56\) | −1.77846 | −0.237656 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.45769 | 0.322711 | ||||||||
\(59\) | 12.1725 | 1.58472 | 0.792360 | − | 0.610054i | \(-0.208852\pi\) | ||||
0.792360 | + | 0.610054i | \(0.208852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 3.30777 | 0.420088 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.16291 | −0.395364 | ||||||||
\(65\) | −0.529317 | −0.0656536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.9379 | −1.94713 | −0.973564 | − | 0.228415i | \(-0.926646\pi\) | ||||
−0.973564 | + | 0.228415i | \(0.926646\pi\) | |||||||
\(68\) | −2.32582 | −0.282047 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.249141 | −0.0297780 | ||||||||
\(71\) | −1.19051 | −0.141287 | −0.0706436 | − | 0.997502i | \(-0.522505\pi\) | ||||
−0.0706436 | + | 0.997502i | \(0.522505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.64315 | 0.894562 | 0.447281 | − | 0.894393i | \(-0.352392\pi\) | ||||
0.447281 | + | 0.894393i | \(0.352392\pi\) | |||||||
\(74\) | 1.11383 | 0.129480 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.61555 | 0.300024 | ||||||||
\(77\) | −2.24914 | −0.256313 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33881 | −0.150628 | −0.0753139 | − | 0.997160i | \(-0.523996\pi\) | ||||
−0.0753139 | + | 0.997160i | \(0.523996\pi\) | |||||||
\(80\) | −1.43965 | −0.160958 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.05863 | 0.337770 | ||||||||
\(83\) | 16.3500 | 1.79464 | 0.897322 | − | 0.441377i | \(-0.145510\pi\) | ||||
0.897322 | + | 0.441377i | \(0.145510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.692226 | −0.0750825 | ||||||||
\(86\) | −5.36297 | −0.578304 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | −6.91033 | −0.732494 | −0.366247 | − | 0.930518i | \(-0.619357\pi\) | ||||
−0.366247 | + | 0.930518i | \(0.619357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 10.3810 | 1.08230 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.04059 | 0.416755 | ||||||||
\(95\) | 0.778457 | 0.0798680 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.47068 | −0.352395 | −0.176197 | − | 0.984355i | \(-0.556380\pi\) | ||||
−0.176197 | + | 0.984355i | \(0.556380\pi\) | |||||||
\(98\) | −0.470683 | −0.0475462 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.39400 | 0.839400 | ||||||||
\(101\) | −7.75086 | −0.771239 | −0.385620 | − | 0.922658i | \(-0.626012\pi\) | ||||
−0.385620 | + | 0.922658i | \(0.626012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9966 | −1.67472 | −0.837361 | − | 0.546651i | \(-0.815902\pi\) | ||||
−0.837361 | + | 0.546651i | \(0.815902\pi\) | |||||||
\(104\) | 1.77846 | 0.174392 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30777 | 0.515537 | ||||||||
\(107\) | 5.55691 | 0.537207 | 0.268604 | − | 0.963251i | \(-0.413438\pi\) | ||||
0.268604 | + | 0.963251i | \(0.413438\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.92332 | 0.758917 | 0.379458 | − | 0.925209i | \(-0.376110\pi\) | ||||
0.379458 | + | 0.925209i | \(0.376110\pi\) | |||||||
\(110\) | 0.560352 | 0.0534275 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.71982 | −0.256999 | ||||||||
\(113\) | 9.89229 | 0.930588 | 0.465294 | − | 0.885156i | \(-0.345949\pi\) | ||||
0.465294 | + | 0.885156i | \(0.345949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.08967 | 0.288113 | ||||||||
\(116\) | 9.28629 | 0.862210 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.72938 | −0.527432 | ||||||||
\(119\) | −1.30777 | −0.119883 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.94137 | −0.540124 | ||||||||
\(122\) | 0.941367 | 0.0852273 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.4983 | 1.12238 | ||||||||
\(125\) | 5.14486 | 0.460171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.824101 | 0.0731271 | 0.0365635 | − | 0.999331i | \(-0.488359\pi\) | ||||
0.0365635 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(128\) | 11.1629 | 0.986671 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.249141 | 0.0218511 | ||||||||
\(131\) | −10.6155 | −0.927485 | −0.463742 | − | 0.885970i | \(-0.653494\pi\) | ||||
−0.463742 | + | 0.885970i | \(0.653494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.47068 | 0.127524 | ||||||||
\(134\) | 7.50172 | 0.648050 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.32582 | 0.199437 | ||||||||
\(137\) | −11.3630 | −0.970804 | −0.485402 | − | 0.874291i | \(-0.661327\pi\) | ||||
−0.485402 | + | 0.874291i | \(0.661327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9233 | −1.18096 | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590480 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(140\) | −0.941367 | −0.0795600 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.560352 | 0.0470237 | ||||||||
\(143\) | 2.24914 | 0.188083 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76385 | 0.229525 | ||||||||
\(146\) | −3.59750 | −0.297731 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.20855 | 0.345941 | ||||||||
\(149\) | −9.30777 | −0.762523 | −0.381261 | − | 0.924467i | \(-0.624510\pi\) | ||||
−0.381261 | + | 0.924467i | \(0.624510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.07324 | 0.575612 | 0.287806 | − | 0.957689i | \(-0.407074\pi\) | ||||
0.287806 | + | 0.957689i | \(0.407074\pi\) | |||||||
\(152\) | −2.61555 | −0.212149 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.05863 | 0.0853071 | ||||||||
\(155\) | 3.71982 | 0.298783 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.04059 | −0.482091 | −0.241046 | − | 0.970514i | \(-0.577490\pi\) | ||||
−0.241046 | + | 0.970514i | \(0.577490\pi\) | |||||||
\(158\) | 0.630155 | 0.0501325 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.56035 | 0.202414 | ||||||||
\(161\) | 5.83709 | 0.460027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.38101 | 0.499800 | 0.249900 | − | 0.968272i | \(-0.419602\pi\) | ||||
0.249900 | + | 0.968272i | \(0.419602\pi\) | |||||||
\(164\) | 11.5569 | 0.902443 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.69566 | −0.597299 | ||||||||
\(167\) | 16.5845 | 1.28335 | 0.641674 | − | 0.766977i | \(-0.278240\pi\) | ||||
0.641674 | + | 0.766977i | \(0.278240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.325819 | 0.0249892 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20.2637 | −1.54510 | ||||||||
\(173\) | 23.3009 | 1.77153 | 0.885767 | − | 0.464130i | \(-0.153633\pi\) | ||||
0.885767 | + | 0.464130i | \(0.153633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.71982 | 0.356785 | ||||||||
\(176\) | 6.11727 | 0.461106 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.25258 | 0.243791 | ||||||||
\(179\) | −21.0422 | −1.57277 | −0.786384 | − | 0.617738i | \(-0.788049\pi\) | ||||
−0.786384 | + | 0.617738i | \(0.788049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7474 | 1.24483 | 0.622413 | − | 0.782689i | \(-0.286152\pi\) | ||||
0.622413 | + | 0.782689i | \(0.286152\pi\) | |||||||
\(182\) | 0.470683 | 0.0348894 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.3810 | −0.765299 | ||||||||
\(185\) | 1.25258 | 0.0920914 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.94137 | 0.215094 | ||||||||
\(188\) | 15.2672 | 1.11347 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.366407 | −0.0265819 | ||||||||
\(191\) | 7.43965 | 0.538314 | 0.269157 | − | 0.963096i | \(-0.413255\pi\) | ||||
0.269157 | + | 0.963096i | \(0.413255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.50172 | −0.108096 | −0.0540480 | − | 0.998538i | \(-0.517212\pi\) | ||||
−0.0540480 | + | 0.998538i | \(0.517212\pi\) | |||||||
\(194\) | 1.63359 | 0.117285 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.77846 | −0.127033 | ||||||||
\(197\) | −23.9931 | −1.70944 | −0.854720 | − | 0.519090i | \(-0.826271\pi\) | ||||
−0.854720 | + | 0.519090i | \(0.826271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.01461 | −0.142812 | −0.0714059 | − | 0.997447i | \(-0.522749\pi\) | ||||
−0.0714059 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(200\) | −8.39400 | −0.593546 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.64820 | 0.256687 | ||||||||
\(203\) | 5.22154 | 0.366480 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.43965 | 0.240235 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.71982 | 0.188586 | ||||||||
\(209\) | −3.30777 | −0.228803 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1008 | 0.695370 | 0.347685 | − | 0.937611i | \(-0.386968\pi\) | ||||
0.347685 | + | 0.937611i | \(0.386968\pi\) | |||||||
\(212\) | 20.0552 | 1.37740 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.61555 | −0.178795 | ||||||||
\(215\) | −6.03104 | −0.411313 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.02760 | 0.477064 | ||||||||
\(218\) | −3.72938 | −0.252585 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.11727 | 0.142746 | ||||||||
\(221\) | 1.30777 | 0.0879704 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1414 | 0.679120 | 0.339560 | − | 0.940584i | \(-0.389722\pi\) | ||||
0.339560 | + | 0.940584i | \(0.389722\pi\) | |||||||
\(224\) | 4.83709 | 0.323192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.65613 | −0.309721 | ||||||||
\(227\) | 5.38445 | 0.357379 | 0.178689 | − | 0.983906i | \(-0.442814\pi\) | ||||
0.178689 | + | 0.983906i | \(0.442814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.32238 | 0.219549 | 0.109775 | − | 0.993957i | \(-0.464987\pi\) | ||||
0.109775 | + | 0.993957i | \(0.464987\pi\) | |||||||
\(230\) | −1.45426 | −0.0958908 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.28629 | −0.609675 | ||||||||
\(233\) | −13.7198 | −0.898816 | −0.449408 | − | 0.893327i | \(-0.648365\pi\) | ||||
−0.449408 | + | 0.893327i | \(0.648365\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.54392 | 0.296413 | ||||||||
\(236\) | −21.6482 | −1.40918 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.615547 | 0.0399000 | ||||||||
\(239\) | 3.50172 | 0.226507 | 0.113254 | − | 0.993566i | \(-0.463873\pi\) | ||||
0.113254 | + | 0.993566i | \(0.463873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58795 | 0.102289 | 0.0511444 | − | 0.998691i | \(-0.483713\pi\) | ||||
0.0511444 | + | 0.998691i | \(0.483713\pi\) | |||||||
\(242\) | 2.79650 | 0.179766 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.55691 | 0.227708 | ||||||||
\(245\) | −0.529317 | −0.0338168 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47068 | −0.0935773 | ||||||||
\(248\) | −12.4983 | −0.793642 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.42160 | −0.153156 | ||||||||
\(251\) | 4.92676 | 0.310974 | 0.155487 | − | 0.987838i | \(-0.450305\pi\) | ||||
0.155487 | + | 0.987838i | \(0.450305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1284 | −0.825378 | ||||||||
\(254\) | −0.387890 | −0.0243384 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.07162 | 0.0669764 | ||||||||
\(257\) | 8.01461 | 0.499938 | 0.249969 | − | 0.968254i | \(-0.419580\pi\) | ||||
0.249969 | + | 0.968254i | \(0.419580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.36641 | 0.147041 | ||||||||
\(260\) | 0.941367 | 0.0583811 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.99656 | 0.308689 | ||||||||
\(263\) | −1.60256 | −0.0988179 | −0.0494090 | − | 0.998779i | \(-0.515734\pi\) | ||||
−0.0494090 | + | 0.998779i | \(0.515734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.96896 | 0.366671 | ||||||||
\(266\) | −0.692226 | −0.0424431 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 28.3449 | 1.73144 | ||||||||
\(269\) | 11.8207 | 0.720719 | 0.360359 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360359 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8827 | 1.32928 | 0.664641 | − | 0.747163i | \(-0.268585\pi\) | ||||
0.664641 | + | 0.747163i | \(0.268585\pi\) | |||||||
\(272\) | 3.55691 | 0.215670 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.34836 | 0.323106 | ||||||||
\(275\) | −10.6155 | −0.640142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2181 | −0.613946 | −0.306973 | − | 0.951718i | \(-0.599316\pi\) | ||||
−0.306973 | + | 0.951718i | \(0.599316\pi\) | |||||||
\(278\) | 6.55348 | 0.393051 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.941367 | 0.0562574 | ||||||||
\(281\) | −1.54231 | −0.0920063 | −0.0460031 | − | 0.998941i | \(-0.514648\pi\) | ||||
−0.0460031 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8466 | 0.941985 | 0.470993 | − | 0.882137i | \(-0.343896\pi\) | ||||
0.470993 | + | 0.882137i | \(0.343896\pi\) | |||||||
\(284\) | 2.11727 | 0.125637 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.05863 | −0.0625983 | ||||||||
\(287\) | 6.49828 | 0.383581 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2897 | −0.899396 | ||||||||
\(290\) | −1.30090 | −0.0763914 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.5930 | −0.795470 | ||||||||
\(293\) | −11.0828 | −0.647464 | −0.323732 | − | 0.946149i | \(-0.604938\pi\) | ||||
−0.323732 | + | 0.946149i | \(0.604938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.44309 | −0.375131 | ||||||||
\(296\) | −4.20855 | −0.244617 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.38101 | 0.253785 | ||||||||
\(299\) | −5.83709 | −0.337568 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3940 | −0.656740 | ||||||||
\(302\) | −3.32926 | −0.191577 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 1.05863 | 0.0606172 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.4121 | 1.16498 | 0.582489 | − | 0.812839i | \(-0.302079\pi\) | ||||
0.582489 | + | 0.812839i | \(0.302079\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.75086 | −0.0994421 | ||||||||
\(311\) | 1.92332 | 0.109062 | 0.0545308 | − | 0.998512i | \(-0.482634\pi\) | ||||
0.0545308 | + | 0.998512i | \(0.482634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3664 | −0.812037 | −0.406019 | − | 0.913865i | \(-0.633083\pi\) | ||||
−0.406019 | + | 0.913865i | \(0.633083\pi\) | |||||||
\(314\) | 2.84320 | 0.160451 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.38101 | 0.133943 | ||||||||
\(317\) | −15.5569 | −0.873763 | −0.436882 | − | 0.899519i | \(-0.643917\pi\) | ||||
−0.436882 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7440 | −0.657537 | ||||||||
\(320\) | 1.67418 | 0.0935895 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.74742 | −0.153108 | ||||||||
\(323\) | −1.92332 | −0.107016 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.71982 | −0.261809 | ||||||||
\(326\) | −3.00344 | −0.166345 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.5569 | −0.638124 | ||||||||
\(329\) | 8.58451 | 0.473279 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5500 | 1.73415 | 0.867073 | − | 0.498180i | \(-0.165998\pi\) | ||||
0.867073 | + | 0.498180i | \(0.165998\pi\) | |||||||
\(332\) | −29.0777 | −1.59585 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.80605 | −0.427128 | ||||||||
\(335\) | 8.43621 | 0.460919 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.42666 | −0.459029 | −0.229515 | − | 0.973305i | \(-0.573714\pi\) | ||||
−0.229515 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(338\) | −0.470683 | −0.0256018 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.23109 | 0.0667655 | ||||||||
\(341\) | −15.8061 | −0.855946 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 20.2637 | 1.09255 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.9673 | −0.589608 | ||||||||
\(347\) | −19.3484 | −1.03867 | −0.519337 | − | 0.854569i | \(-0.673821\pi\) | ||||
−0.519337 | + | 0.854569i | \(0.673821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2553 | 1.45894 | 0.729470 | − | 0.684013i | \(-0.239767\pi\) | ||||
0.729470 | + | 0.684013i | \(0.239767\pi\) | |||||||
\(350\) | −2.22154 | −0.118746 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.8793 | −0.579868 | ||||||||
\(353\) | 25.6742 | 1.36650 | 0.683249 | − | 0.730185i | \(-0.260566\pi\) | ||||
0.683249 | + | 0.730185i | \(0.260566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.630155 | 0.0334452 | ||||||||
\(356\) | 12.2897 | 0.651354 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.90422 | 0.523454 | ||||||||
\(359\) | 23.4182 | 1.23596 | 0.617982 | − | 0.786192i | \(-0.287951\pi\) | ||||
0.617982 | + | 0.786192i | \(0.287951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8371 | −0.886163 | ||||||||
\(362\) | −7.88273 | −0.414307 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.77846 | 0.0932165 | ||||||||
\(365\) | −4.04564 | −0.211759 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6854 | −0.766569 | −0.383285 | − | 0.923630i | \(-0.625207\pi\) | ||||
−0.383285 | + | 0.923630i | \(0.625207\pi\) | |||||||
\(368\) | −15.8759 | −0.827586 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.589568 | −0.0306502 | ||||||||
\(371\) | 11.2767 | 0.585459 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.6673 | −1.22545 | −0.612723 | − | 0.790298i | \(-0.709926\pi\) | ||||
−0.612723 | + | 0.790298i | \(0.709926\pi\) | |||||||
\(374\) | −1.38445 | −0.0715883 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.2672 | −0.787345 | ||||||||
\(377\) | −5.22154 | −0.268923 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.7405 | −1.68177 | −0.840884 | − | 0.541215i | \(-0.817965\pi\) | ||||
−0.840884 | + | 0.541215i | \(0.817965\pi\) | |||||||
\(380\) | −1.38445 | −0.0710209 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.50172 | −0.179164 | ||||||||
\(383\) | 22.6155 | 1.15560 | 0.577800 | − | 0.816178i | \(-0.303911\pi\) | ||||
0.577800 | + | 0.816178i | \(0.303911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19051 | 0.0606739 | ||||||||
\(386\) | 0.706834 | 0.0359769 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.17246 | 0.313359 | ||||||||
\(389\) | −38.0483 | −1.92913 | −0.964563 | − | 0.263852i | \(-0.915007\pi\) | ||||
−0.964563 | + | 0.263852i | \(0.915007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.63359 | −0.386047 | ||||||||
\(392\) | 1.77846 | 0.0898256 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.2932 | 0.568941 | ||||||||
\(395\) | 0.708654 | 0.0356562 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.7052 | −0.587468 | −0.293734 | − | 0.955887i | \(-0.594898\pi\) | ||||
−0.293734 | + | 0.955887i | \(0.594898\pi\) | |||||||
\(398\) | 0.948243 | 0.0475311 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.8371 | −0.641855 | ||||||||
\(401\) | −3.55691 | −0.177624 | −0.0888119 | − | 0.996048i | \(-0.528307\pi\) | ||||
−0.0888119 | + | 0.996048i | \(0.528307\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.02760 | −0.350070 | ||||||||
\(404\) | 13.7846 | 0.685808 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.45769 | −0.121973 | ||||||||
\(407\) | −5.32238 | −0.263821 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.26213 | 0.260196 | 0.130098 | − | 0.991501i | \(-0.458471\pi\) | ||||
0.130098 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(410\) | −1.61899 | −0.0799560 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.2277 | 1.48921 | ||||||||
\(413\) | −12.1725 | −0.598968 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.65432 | −0.424824 | ||||||||
\(416\) | −4.83709 | −0.237158 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.55691 | 0.0761512 | ||||||||
\(419\) | −26.0337 | −1.27183 | −0.635915 | − | 0.771759i | \(-0.719377\pi\) | ||||
−0.635915 | + | 0.771759i | \(0.719377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2423 | 1.08402 | 0.542011 | − | 0.840372i | \(-0.317663\pi\) | ||||
0.542011 | + | 0.840372i | \(0.317663\pi\) | |||||||
\(422\) | −4.75430 | −0.231436 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.0552 | −0.973966 | ||||||||
\(425\) | −6.17246 | −0.299408 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.00000 | 0.0967868 | ||||||||
\(428\) | −9.88273 | −0.477700 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.83871 | 0.136895 | ||||||||
\(431\) | −27.6742 | −1.33302 | −0.666509 | − | 0.745497i | \(-0.732212\pi\) | ||||
−0.666509 | + | 0.745497i | \(0.732212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.7880 | −0.614552 | −0.307276 | − | 0.951620i | \(-0.599418\pi\) | ||||
−0.307276 | + | 0.951620i | \(0.599418\pi\) | |||||||
\(434\) | −3.30777 | −0.158778 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.0913 | −0.674850 | ||||||||
\(437\) | 8.58451 | 0.410653 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1656 | −0.866996 | −0.433498 | − | 0.901155i | \(-0.642721\pi\) | ||||
−0.433498 | + | 0.901155i | \(0.642721\pi\) | |||||||
\(440\) | −2.11727 | −0.100937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.615547 | −0.0292786 | ||||||||
\(443\) | −0.107714 | −0.00511767 | −0.00255883 | − | 0.999997i | \(-0.500815\pi\) | ||||
−0.00255883 | + | 0.999997i | \(0.500815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.65775 | 0.173394 | ||||||||
\(446\) | −4.77340 | −0.226027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.16291 | 0.149433 | ||||||||
\(449\) | 22.1725 | 1.04638 | 0.523192 | − | 0.852215i | \(-0.324741\pi\) | ||||
0.523192 | + | 0.852215i | \(0.324741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.6155 | −0.688219 | ||||||||
\(452\) | −17.5930 | −0.827505 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.53437 | −0.118944 | ||||||||
\(455\) | 0.529317 | 0.0248147 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.35953 | 0.203930 | 0.101965 | − | 0.994788i | \(-0.467487\pi\) | ||||
0.101965 | + | 0.994788i | \(0.467487\pi\) | |||||||
\(458\) | −1.56379 | −0.0730711 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.49484 | −0.256198 | ||||||||
\(461\) | −32.3810 | −1.50813 | −0.754067 | − | 0.656797i | \(-0.771911\pi\) | ||||
−0.754067 | + | 0.656797i | \(0.771911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.36641 | 0.388820 | 0.194410 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194410 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(464\) | −14.2017 | −0.659296 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.45769 | 0.299147 | ||||||||
\(467\) | 19.5423 | 0.904310 | 0.452155 | − | 0.891939i | \(-0.350655\pi\) | ||||
0.452155 | + | 0.891939i | \(0.350655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.9379 | 0.735945 | ||||||||
\(470\) | −2.13875 | −0.0986532 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.6482 | 0.996439 | ||||||||
\(473\) | 25.6267 | 1.17832 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.94137 | 0.318492 | ||||||||
\(476\) | 2.32582 | 0.106604 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.64820 | −0.0753870 | ||||||||
\(479\) | 28.5224 | 1.30322 | 0.651612 | − | 0.758553i | \(-0.274093\pi\) | ||||
0.651612 | + | 0.758553i | \(0.274093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.36641 | −0.107899 | ||||||||
\(482\) | −0.747422 | −0.0340441 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5665 | 0.480294 | ||||||||
\(485\) | 1.83709 | 0.0834180 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8241 | 1.12489 | 0.562444 | − | 0.826836i | \(-0.309861\pi\) | ||||
0.562444 | + | 0.826836i | \(0.309861\pi\) | |||||||
\(488\) | −3.55691 | −0.161014 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.249141 | 0.0112550 | ||||||||
\(491\) | −29.1690 | −1.31638 | −0.658190 | − | 0.752852i | \(-0.728678\pi\) | ||||
−0.658190 | + | 0.752852i | \(0.728678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.82860 | −0.307545 | ||||||||
\(494\) | 0.692226 | 0.0311447 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.1138 | −0.858236 | ||||||||
\(497\) | 1.19051 | 0.0534016 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.3009 | −1.49075 | −0.745376 | − | 0.666644i | \(-0.767730\pi\) | ||||
−0.745376 | + | 0.666644i | \(0.767730\pi\) | |||||||
\(500\) | −9.14992 | −0.409197 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.31894 | −0.103500 | ||||||||
\(503\) | 12.3258 | 0.549581 | 0.274791 | − | 0.961504i | \(-0.411391\pi\) | ||||
0.274791 | + | 0.961504i | \(0.411391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.10266 | 0.182566 | ||||||||
\(506\) | 6.17934 | 0.274705 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.46563 | −0.0650267 | ||||||||
\(509\) | −23.7052 | −1.05072 | −0.525358 | − | 0.850882i | \(-0.676068\pi\) | ||||
−0.525358 | + | 0.850882i | \(0.676068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.64315 | −0.338113 | ||||||||
\(512\) | −22.8302 | −1.00896 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.77234 | −0.166391 | ||||||||
\(515\) | 8.99656 | 0.396436 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3078 | −0.849155 | ||||||||
\(518\) | −1.11383 | −0.0489388 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.941367 | −0.0412817 | ||||||||
\(521\) | −43.9018 | −1.92337 | −0.961687 | − | 0.274149i | \(-0.911604\pi\) | ||||
−0.961687 | + | 0.274149i | \(0.911604\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.4328 | 1.63682 | 0.818410 | − | 0.574634i | \(-0.194856\pi\) | ||||
0.818410 | + | 0.574634i | \(0.194856\pi\) | |||||||
\(524\) | 18.8793 | 0.824746 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.754297 | 0.0328889 | ||||||||
\(527\) | −9.19051 | −0.400345 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0716 | 0.481375 | ||||||||
\(530\) | −2.80949 | −0.122037 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.61555 | −0.113398 | ||||||||
\(533\) | −6.49828 | −0.281472 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.94137 | −0.127166 | ||||||||
\(536\) | −28.3449 | −1.22431 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.56379 | −0.239872 | ||||||||
\(539\) | 2.24914 | 0.0968773 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.9751 | −1.50370 | −0.751848 | − | 0.659336i | \(-0.770837\pi\) | ||||
−0.751848 | + | 0.659336i | \(0.770837\pi\) | |||||||
\(542\) | −10.2998 | −0.442416 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.32582 | −0.271217 | ||||||||
\(545\) | −4.19395 | −0.179649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.50783 | 0.278255 | 0.139127 | − | 0.990274i | \(-0.455570\pi\) | ||||
0.139127 | + | 0.990274i | \(0.455570\pi\) | |||||||
\(548\) | 20.2086 | 0.863267 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.99656 | 0.213054 | ||||||||
\(551\) | 7.67924 | 0.327146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.33881 | 0.0569320 | ||||||||
\(554\) | 4.80949 | 0.204336 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.7620 | 1.05014 | ||||||||
\(557\) | 43.4328 | 1.84031 | 0.920153 | − | 0.391559i | \(-0.128064\pi\) | ||||
0.920153 | + | 0.391559i | \(0.128064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3940 | 0.481915 | ||||||||
\(560\) | 1.43965 | 0.0608362 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.725938 | 0.0306218 | ||||||||
\(563\) | 33.8827 | 1.42799 | 0.713993 | − | 0.700152i | \(-0.246885\pi\) | ||||
0.713993 | + | 0.700152i | \(0.246885\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.23615 | −0.220287 | ||||||||
\(566\) | −7.45875 | −0.313515 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.11727 | −0.0888385 | ||||||||
\(569\) | −19.2147 | −0.805521 | −0.402760 | − | 0.915305i | \(-0.631949\pi\) | ||||
−0.402760 | + | 0.915305i | \(0.631949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8268 | 0.871573 | 0.435787 | − | 0.900050i | \(-0.356470\pi\) | ||||
0.435787 | + | 0.900050i | \(0.356470\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.05863 | −0.127665 | ||||||||
\(575\) | 27.5500 | 1.14892 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.6448 | 1.19250 | 0.596249 | − | 0.802800i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802800i | \(0.296657\pi\) | |||||||
\(578\) | 7.19662 | 0.299340 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.91539 | −0.204100 | ||||||||
\(581\) | −16.3500 | −0.678311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3630 | −1.05043 | ||||||||
\(584\) | 13.5930 | 0.562483 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.21649 | 0.215491 | ||||||||
\(587\) | 4.32076 | 0.178337 | 0.0891685 | − | 0.996017i | \(-0.471579\pi\) | ||||
0.0891685 | + | 0.996017i | \(0.471579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.3354 | 0.425862 | ||||||||
\(590\) | 3.03265 | 0.124852 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.43621 | −0.264527 | ||||||||
\(593\) | 15.9690 | 0.655767 | 0.327883 | − | 0.944718i | \(-0.393665\pi\) | ||||
0.327883 | + | 0.944718i | \(0.393665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.692226 | 0.0283785 | ||||||||
\(596\) | 16.5535 | 0.678057 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.74742 | 0.112350 | ||||||||
\(599\) | 16.8697 | 0.689279 | 0.344640 | − | 0.938735i | \(-0.388001\pi\) | ||||
0.344640 | + | 0.938735i | \(0.388001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3415 | −0.625792 | −0.312896 | − | 0.949787i | \(-0.601299\pi\) | ||||
−0.312896 | + | 0.949787i | \(0.601299\pi\) | |||||||
\(602\) | 5.36297 | 0.218578 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.5795 | −0.511851 | ||||||||
\(605\) | 3.14486 | 0.127857 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8353 | 1.45451 | 0.727254 | − | 0.686368i | \(-0.240796\pi\) | ||||
0.727254 | + | 0.686368i | \(0.240796\pi\) | |||||||
\(608\) | 7.11383 | 0.288504 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.498281 | −0.0201748 | ||||||||
\(611\) | −8.58451 | −0.347292 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6673 | 0.794355 | 0.397177 | − | 0.917742i | \(-0.369990\pi\) | ||||
0.397177 | + | 0.917742i | \(0.369990\pi\) | |||||||
\(614\) | −9.60761 | −0.387732 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 41.4588 | 1.66907 | 0.834533 | − | 0.550958i | \(-0.185737\pi\) | ||||
0.834533 | + | 0.550958i | \(0.185737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8793 | 0.437276 | 0.218638 | − | 0.975806i | \(-0.429839\pi\) | ||||
0.218638 | + | 0.975806i | \(0.429839\pi\) | |||||||
\(620\) | −6.61555 | −0.265687 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.905275 | −0.0362982 | ||||||||
\(623\) | 6.91033 | 0.276857 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8759 | 0.835034 | ||||||||
\(626\) | 6.76203 | 0.270265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.7429 | 0.428689 | ||||||||
\(629\) | −3.09472 | −0.123395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4396 | −1.25159 | −0.625796 | − | 0.779987i | \(-0.715226\pi\) | ||||
−0.625796 | + | 0.779987i | \(0.715226\pi\) | |||||||
\(632\) | −2.38101 | −0.0947117 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.32238 | 0.290809 | ||||||||
\(635\) | −0.436210 | −0.0173105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 5.52770 | 0.218844 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.90871 | −0.233562 | ||||||||
\(641\) | −3.04221 | −0.120160 | −0.0600799 | − | 0.998194i | \(-0.519136\pi\) | ||||
−0.0600799 | + | 0.998194i | \(0.519136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.02922 | 0.316641 | 0.158321 | − | 0.987388i | \(-0.449392\pi\) | ||||
0.158321 | + | 0.987388i | \(0.449392\pi\) | |||||||
\(644\) | −10.3810 | −0.409069 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.905275 | 0.0356176 | ||||||||
\(647\) | −7.07324 | −0.278078 | −0.139039 | − | 0.990287i | \(-0.544401\pi\) | ||||
−0.139039 | + | 0.990287i | \(0.544401\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3776 | 1.07466 | ||||||||
\(650\) | 2.22154 | 0.0871361 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3484 | −0.444436 | ||||||||
\(653\) | 15.7586 | 0.616681 | 0.308341 | − | 0.951276i | \(-0.400226\pi\) | ||||
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.61899 | 0.219552 | ||||||||
\(656\) | −17.6742 | −0.690061 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.04059 | −0.157518 | ||||||||
\(659\) | 12.2181 | 0.475950 | 0.237975 | − | 0.971271i | \(-0.423516\pi\) | ||||
0.237975 | + | 0.971271i | \(0.423516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.73443 | 0.145253 | 0.0726263 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726263 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(662\) | −14.8501 | −0.577165 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.0777 | 1.12844 | ||||||||
\(665\) | −0.778457 | −0.0301873 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.4786 | 1.18014 | ||||||||
\(668\) | −29.4948 | −1.14119 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.97078 | −0.153405 | ||||||||
\(671\) | −4.49828 | −0.173654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.65775 | −0.218090 | −0.109045 | − | 0.994037i | \(-0.534779\pi\) | ||||
−0.109045 | + | 0.994037i | \(0.534779\pi\) | |||||||
\(674\) | 3.96629 | 0.152776 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.77846 | −0.0684022 | ||||||||
\(677\) | −9.39906 | −0.361235 | −0.180618 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180618 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.47068 | 0.133193 | ||||||||
\(680\) | −1.23109 | −0.0472103 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.43965 | 0.284879 | ||||||||
\(683\) | 20.7328 | 0.793319 | 0.396660 | − | 0.917966i | \(-0.370169\pi\) | ||||
0.396660 | + | 0.917966i | \(0.370169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.01461 | 0.229806 | ||||||||
\(686\) | 0.470683 | 0.0179708 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.9897 | 1.18147 | ||||||||
\(689\) | −11.2767 | −0.429610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0862 | 0.611949 | 0.305975 | − | 0.952040i | \(-0.401018\pi\) | ||||
0.305975 | + | 0.952040i | \(0.401018\pi\) | |||||||
\(692\) | −41.4396 | −1.57530 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.10695 | 0.345695 | ||||||||
\(695\) | 7.36984 | 0.279554 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.49828 | −0.321895 | ||||||||
\(698\) | −12.8286 | −0.485570 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.39400 | −0.317264 | ||||||||
\(701\) | 6.98013 | 0.263636 | 0.131818 | − | 0.991274i | \(-0.457919\pi\) | ||||
0.131818 | + | 0.991274i | \(0.457919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.48024 | 0.131260 | ||||||||
\(704\) | −7.11383 | −0.268112 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0844 | −0.454803 | ||||||||
\(707\) | 7.75086 | 0.291501 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.39239 | 0.315183 | 0.157591 | − | 0.987504i | \(-0.449627\pi\) | ||||
0.157591 | + | 0.987504i | \(0.449627\pi\) | |||||||
\(710\) | −0.296604 | −0.0111313 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.2897 | −0.460577 | ||||||||
\(713\) | 41.0207 | 1.53624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.19051 | −0.0445225 | ||||||||
\(716\) | 37.4227 | 1.39855 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.0225 | −0.411358 | ||||||||
\(719\) | 5.16129 | 0.192484 | 0.0962418 | − | 0.995358i | \(-0.469318\pi\) | ||||
0.0962418 | + | 0.995358i | \(0.469318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.9966 | 0.632985 | ||||||||
\(722\) | 7.92494 | 0.294936 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.7846 | −1.10693 | ||||||||
\(725\) | 24.6448 | 0.915284 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.4362 | −1.49970 | −0.749848 | − | 0.661610i | \(-0.769873\pi\) | ||||
−0.749848 | + | 0.661610i | \(0.769873\pi\) | |||||||
\(728\) | −1.77846 | −0.0659140 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.90422 | 0.0704782 | ||||||||
\(731\) | 14.9008 | 0.551125 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.1311 | −1.44534 | −0.722670 | − | 0.691193i | \(-0.757085\pi\) | ||||
−0.722670 | + | 0.691193i | \(0.757085\pi\) | |||||||
\(734\) | 6.91215 | 0.255132 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.2345 | 1.04074 | ||||||||
\(737\) | −35.8466 | −1.32043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.13531 | −0.262477 | −0.131238 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131238 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(740\) | −2.22766 | −0.0818903 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.30777 | −0.194855 | ||||||||
\(743\) | −13.8827 | −0.509308 | −0.254654 | − | 0.967032i | \(-0.581962\pi\) | ||||
−0.254654 | + | 0.967032i | \(0.581962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.92676 | 0.180502 | ||||||||
\(746\) | 11.1398 | 0.407857 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.23109 | −0.191268 | ||||||||
\(749\) | −5.55691 | −0.203045 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.3251 | −1.36201 | −0.681005 | − | 0.732278i | \(-0.738457\pi\) | ||||
−0.681005 | + | 0.732278i | \(0.738457\pi\) | |||||||
\(752\) | −23.3484 | −0.851427 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.45769 | 0.0895039 | ||||||||
\(755\) | −3.74398 | −0.136258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.10428 | −0.258209 | −0.129105 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129105 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(758\) | 15.4104 | 0.559732 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.38445 | 0.0502194 | ||||||||
\(761\) | 25.9621 | 0.941125 | 0.470562 | − | 0.882367i | \(-0.344051\pi\) | ||||
0.470562 | + | 0.882367i | \(0.344051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.92332 | −0.286843 | ||||||||
\(764\) | −13.2311 | −0.478684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6448 | −0.384611 | ||||||||
\(767\) | 12.1725 | 0.439522 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.4638 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(770\) | −0.560352 | −0.0201937 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.67074 | 0.0961221 | ||||||||
\(773\) | 40.4914 | 1.45637 | 0.728187 | − | 0.685378i | \(-0.240363\pi\) | ||||
0.728187 | + | 0.685378i | \(0.240363\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.1690 | 1.19147 | ||||||||
\(776\) | −6.17246 | −0.221578 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.9087 | 0.642058 | ||||||||
\(779\) | 9.55691 | 0.342412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.67762 | −0.0958127 | ||||||||
\(782\) | 3.59301 | 0.128486 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.71982 | 0.0971366 | ||||||||
\(785\) | 3.19738 | 0.114119 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.02072 | −0.178969 | −0.0894847 | − | 0.995988i | \(-0.528522\pi\) | ||||
−0.0894847 | + | 0.995988i | \(0.528522\pi\) | |||||||
\(788\) | 42.6707 | 1.52008 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.333552 | −0.0118672 | ||||||||
\(791\) | −9.89229 | −0.351729 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | 5.50945 | 0.195523 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.58289 | 0.126992 | ||||||||
\(797\) | −19.7002 | −0.697815 | −0.348908 | − | 0.937157i | \(-0.613447\pi\) | ||||
−0.348908 | + | 0.937157i | \(0.613447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.2266 | −0.397169 | ||||||||
\(800\) | 22.8302 | 0.807170 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.67418 | 0.0591174 | ||||||||
\(803\) | 17.1905 | 0.606640 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.08967 | −0.108897 | ||||||||
\(806\) | 3.30777 | 0.116511 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.7846 | −0.484940 | ||||||||
\(809\) | 2.57678 | 0.0905947 | 0.0452974 | − | 0.998974i | \(-0.485576\pi\) | ||||
0.0452974 | + | 0.998974i | \(0.485576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.2311 | 1.44782 | 0.723910 | − | 0.689895i | \(-0.242343\pi\) | ||||
0.723910 | + | 0.689895i | \(0.242343\pi\) | |||||||
\(812\) | −9.28629 | −0.325885 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.50516 | 0.0878057 | ||||||||
\(815\) | −3.37758 | −0.118311 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.7570 | −0.586252 | ||||||||
\(818\) | −2.47680 | −0.0865992 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.11727 | −0.213624 | ||||||||
\(821\) | −5.26719 | −0.183826 | −0.0919130 | − | 0.995767i | \(-0.529298\pi\) | ||||
−0.0919130 | + | 0.995767i | \(0.529298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0191 | 1.25555 | 0.627774 | − | 0.778396i | \(-0.283966\pi\) | ||||
0.627774 | + | 0.778396i | \(0.283966\pi\) | |||||||
\(824\) | −30.2277 | −1.05303 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.72938 | 0.199350 | ||||||||
\(827\) | 16.3157 | 0.567353 | 0.283676 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283676 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.3956 | −1.05568 | −0.527842 | − | 0.849343i | \(-0.676999\pi\) | ||||
−0.527842 | + | 0.849343i | \(0.676999\pi\) | |||||||
\(830\) | 4.07344 | 0.141391 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.16291 | −0.109654 | ||||||||
\(833\) | 1.30777 | 0.0453117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.77846 | −0.303791 | ||||||||
\(836\) | 5.88273 | 0.203459 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.2536 | 0.423295 | ||||||||
\(839\) | −29.8398 | −1.03018 | −0.515092 | − | 0.857135i | \(-0.672242\pi\) | ||||
−0.515092 | + | 0.857135i | \(0.672242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.73549 | −0.0598445 | ||||||||
\(842\) | −10.4691 | −0.360788 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.9639 | −0.618343 | ||||||||
\(845\) | −0.529317 | −0.0182090 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.94137 | 0.204148 | ||||||||
\(848\) | −30.6707 | −1.05324 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.90528 | 0.0996501 | ||||||||
\(851\) | 13.8129 | 0.473501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.203497 | −0.00696761 | −0.00348380 | − | 0.999994i | \(-0.501109\pi\) | ||||
−0.00348380 | + | 0.999994i | \(0.501109\pi\) | |||||||
\(854\) | −0.941367 | −0.0322129 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.88273 | 0.337785 | ||||||||
\(857\) | 12.6155 | 0.430939 | 0.215469 | − | 0.976511i | \(-0.430872\pi\) | ||||
0.215469 | + | 0.976511i | \(0.430872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.9671 | −0.954227 | −0.477113 | − | 0.878842i | \(-0.658317\pi\) | ||||
−0.477113 | + | 0.878842i | \(0.658317\pi\) | |||||||
\(860\) | 10.7259 | 0.365751 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.0258 | 0.443660 | ||||||||
\(863\) | 2.76891 | 0.0942546 | 0.0471273 | − | 0.998889i | \(-0.484993\pi\) | ||||
0.0471273 | + | 0.998889i | \(0.484993\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3336 | −0.419353 | ||||||||
\(866\) | 6.01910 | 0.204537 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.4983 | −0.424219 | ||||||||
\(869\) | −3.01117 | −0.102147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.9379 | −0.540036 | ||||||||
\(872\) | 14.0913 | 0.477191 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.04059 | −0.136675 | ||||||||
\(875\) | −5.14486 | −0.173928 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.71133 | 0.226626 | 0.113313 | − | 0.993559i | \(-0.463854\pi\) | ||||
0.113313 | + | 0.993559i | \(0.463854\pi\) | |||||||
\(878\) | 8.55024 | 0.288557 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.23797 | −0.109152 | ||||||||
\(881\) | 18.3741 | 0.619040 | 0.309520 | − | 0.950893i | \(-0.399832\pi\) | ||||
0.309520 | + | 0.950893i | \(0.399832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.93105 | 0.334207 | 0.167103 | − | 0.985939i | \(-0.446559\pi\) | ||||
0.167103 | + | 0.985939i | \(0.446559\pi\) | |||||||
\(884\) | −2.32582 | −0.0782258 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.0506994 | 0.00170328 | ||||||||
\(887\) | 51.3776 | 1.72509 | 0.862545 | − | 0.505980i | \(-0.168869\pi\) | ||||
0.862545 | + | 0.505980i | \(0.168869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.824101 | −0.0276394 | ||||||||
\(890\) | −1.72164 | −0.0577096 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.0361 | −0.603893 | ||||||||
\(893\) | 12.6251 | 0.422483 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1380 | 0.372302 | ||||||||
\(896\) | −11.1629 | −0.372927 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.4362 | −0.348261 | ||||||||
\(899\) | 36.6949 | 1.22384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.7474 | −0.491308 | ||||||||
\(902\) | 6.87930 | 0.229055 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.5930 | 0.585135 | ||||||||
\(905\) | −8.86469 | −0.294672 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.34225 | 0.144182 | 0.0720910 | − | 0.997398i | \(-0.477033\pi\) | ||||
0.0720910 | + | 0.997398i | \(0.477033\pi\) | |||||||
\(908\) | −9.57602 | −0.317791 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.249141 | −0.00825893 | ||||||||
\(911\) | −31.4853 | −1.04315 | −0.521577 | − | 0.853204i | \(-0.674656\pi\) | ||||
−0.521577 | + | 0.853204i | \(0.674656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.7734 | 1.21702 | ||||||||
\(914\) | −2.05196 | −0.0678728 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.90871 | −0.195229 | ||||||||
\(917\) | 10.6155 | 0.350556 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4588 | 1.43357 | 0.716786 | − | 0.697293i | \(-0.245612\pi\) | ||||
0.716786 | + | 0.697293i | \(0.245612\pi\) | |||||||
\(920\) | 5.49484 | 0.181160 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.2412 | 0.501942 | ||||||||
\(923\) | −1.19051 | −0.0391860 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1690 | 0.367235 | ||||||||
\(926\) | −3.93793 | −0.129408 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.2571 | 0.829104 | ||||||||
\(929\) | −4.40517 | −0.144529 | −0.0722645 | − | 0.997385i | \(-0.523023\pi\) | ||||
−0.0722645 | + | 0.997385i | \(0.523023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47068 | −0.0481997 | ||||||||
\(932\) | 24.4001 | 0.799252 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.19824 | −0.300976 | ||||||||
\(935\) | −1.55691 | −0.0509165 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0990 | −1.11397 | −0.556983 | − | 0.830524i | \(-0.688041\pi\) | ||||
−0.556983 | + | 0.830524i | \(0.688041\pi\) | |||||||
\(938\) | −7.50172 | −0.244940 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.08117 | −0.263579 | ||||||||
\(941\) | −44.4672 | −1.44959 | −0.724795 | − | 0.688964i | \(-0.758066\pi\) | ||||
−0.724795 | + | 0.688964i | \(0.758066\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.9311 | 1.23521 | ||||||||
\(944\) | 33.1070 | 1.07754 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0621 | −0.392172 | ||||||||
\(947\) | −57.9311 | −1.88251 | −0.941253 | − | 0.337702i | \(-0.890350\pi\) | ||||
−0.941253 | + | 0.337702i | \(0.890350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.64315 | 0.248107 | ||||||||
\(950\) | −3.26719 | −0.106002 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.32582 | −0.0753802 | ||||||||
\(953\) | −35.3060 | −1.14367 | −0.571836 | − | 0.820368i | \(-0.693769\pi\) | ||||
−0.571836 | + | 0.820368i | \(0.693769\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.93793 | −0.127428 | ||||||||
\(956\) | −6.22766 | −0.201417 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.4250 | −0.433743 | ||||||||
\(959\) | 11.3630 | 0.366929 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.3871 | 0.593133 | ||||||||
\(962\) | 1.11383 | 0.0359113 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.82410 | −0.0909582 | ||||||||
\(965\) | 0.794885 | 0.0255882 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7148 | 0.762616 | 0.381308 | − | 0.924448i | \(-0.375474\pi\) | ||||
0.381308 | + | 0.924448i | \(0.375474\pi\) | |||||||
\(968\) | −10.5665 | −0.339619 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.864688 | −0.0277635 | ||||||||
\(971\) | 23.9379 | 0.768205 | 0.384102 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384102 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9233 | 0.446361 | ||||||||
\(974\) | −11.6843 | −0.374389 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.43965 | −0.174119 | ||||||||
\(977\) | 16.1871 | 0.517870 | 0.258935 | − | 0.965895i | \(-0.416628\pi\) | ||||
0.258935 | + | 0.965895i | \(0.416628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5423 | −0.496734 | ||||||||
\(980\) | 0.941367 | 0.0300709 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.7294 | 0.438122 | ||||||||
\(983\) | −45.7243 | −1.45838 | −0.729190 | − | 0.684312i | \(-0.760103\pi\) | ||||
−0.729190 | + | 0.684312i | \(0.760103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7000 | 0.404654 | ||||||||
\(986\) | 3.21411 | 0.102358 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.61555 | 0.0832116 | ||||||||
\(989\) | −66.5078 | −2.11483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.40356 | −0.171650 | −0.0858248 | − | 0.996310i | \(-0.527353\pi\) | ||||
−0.0858248 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(992\) | 33.9931 | 1.07928 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.560352 | −0.0177733 | ||||||||
\(995\) | 1.06637 | 0.0338061 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.04832 | 0.191552 | 0.0957761 | − | 0.995403i | \(-0.469467\pi\) | ||||
0.0957761 | + | 0.995403i | \(0.469467\pi\) | |||||||
\(998\) | 15.6742 | 0.496158 | ||||||||
\(999\) | 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 | 819.2.a.i.1.2 | 3 | ||
3.2 | odd | 2 | 91.2.a.d.1.2 | ✓ | 3 | ||
7.6 | odd | 2 | 5733.2.a.x.1.2 | 3 | |||
12.11 | even | 2 | 1456.2.a.t.1.1 | 3 | |||
15.14 | odd | 2 | 2275.2.a.m.1.2 | 3 | |||
21.2 | odd | 6 | 637.2.e.j.508.2 | 6 | |||
21.5 | even | 6 | 637.2.e.i.508.2 | 6 | |||
21.11 | odd | 6 | 637.2.e.j.79.2 | 6 | |||
21.17 | even | 6 | 637.2.e.i.79.2 | 6 | |||
21.20 | even | 2 | 637.2.a.j.1.2 | 3 | |||
24.5 | odd | 2 | 5824.2.a.by.1.1 | 3 | |||
24.11 | even | 2 | 5824.2.a.bs.1.3 | 3 | |||
39.5 | even | 4 | 1183.2.c.f.337.3 | 6 | |||
39.8 | even | 4 | 1183.2.c.f.337.4 | 6 | |||
39.38 | odd | 2 | 1183.2.a.i.1.2 | 3 | |||
273.272 | even | 2 | 8281.2.a.bg.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.d.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
637.2.a.j.1.2 | 3 | 21.20 | even | 2 | |||
637.2.e.i.79.2 | 6 | 21.17 | even | 6 | |||
637.2.e.i.508.2 | 6 | 21.5 | even | 6 | |||
637.2.e.j.79.2 | 6 | 21.11 | odd | 6 | |||
637.2.e.j.508.2 | 6 | 21.2 | odd | 6 | |||
819.2.a.i.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1183.2.a.i.1.2 | 3 | 39.38 | odd | 2 | |||
1183.2.c.f.337.3 | 6 | 39.5 | even | 4 | |||
1183.2.c.f.337.4 | 6 | 39.8 | even | 4 | |||
1456.2.a.t.1.1 | 3 | 12.11 | even | 2 | |||
2275.2.a.m.1.2 | 3 | 15.14 | odd | 2 | |||
5733.2.a.x.1.2 | 3 | 7.6 | odd | 2 | |||
5824.2.a.bs.1.3 | 3 | 24.11 | even | 2 | |||
5824.2.a.by.1.1 | 3 | 24.5 | odd | 2 | |||
8281.2.a.bg.1.2 | 3 | 273.272 | even | 2 |