Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3864) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.167449\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.167449 | −0.0748856 | −0.0374428 | − | 0.999299i | \(-0.511921\pi\) | ||||
−0.0374428 | + | 0.999299i | \(0.511921\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.80451 | 0.544081 | 0.272040 | − | 0.962286i | \(-0.412302\pi\) | ||||
0.272040 | + | 0.962286i | \(0.412302\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.63706 | −1.00874 | −0.504370 | − | 0.863488i | \(-0.668275\pi\) | ||||
−0.504370 | + | 0.863488i | \(0.668275\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.167449 | −0.0432352 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.13941 | 1.00395 | 0.501977 | − | 0.864881i | \(-0.332606\pi\) | ||||
0.501977 | + | 0.864881i | \(0.332606\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.80451 | −1.33165 | −0.665823 | − | 0.746110i | \(-0.731919\pi\) | ||||
−0.665823 | + | 0.746110i | \(0.731919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97196 | −0.994392 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.195488 | −0.0351108 | −0.0175554 | − | 0.999846i | \(-0.505588\pi\) | ||||
−0.0175554 | + | 0.999846i | \(0.505588\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.80451 | 0.314125 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.167449 | 0.0283041 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.33490 | −0.548254 | −0.274127 | − | 0.961694i | \(-0.588389\pi\) | ||||
−0.274127 | + | 0.961694i | \(0.588389\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.63706 | −0.582396 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.94392 | −0.772111 | −0.386055 | − | 0.922476i | \(-0.626163\pi\) | ||||
−0.386055 | + | 0.922476i | \(0.626163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.30216 | −0.198578 | −0.0992891 | − | 0.995059i | \(-0.531657\pi\) | ||||
−0.0992891 | + | 0.995059i | \(0.531657\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.167449 | −0.0249619 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.13941 | 0.457930 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.13941 | 0.579633 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.30686 | 0.454232 | 0.227116 | − | 0.973868i | \(-0.427070\pi\) | ||||
0.227116 | + | 0.973868i | \(0.427070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.302164 | −0.0407438 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.80451 | −0.768826 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.91588 | 0.639993 | 0.319997 | − | 0.947419i | \(-0.396318\pi\) | ||||
0.319997 | + | 0.947419i | \(0.396318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.77647 | 1.12371 | 0.561856 | − | 0.827235i | \(-0.310087\pi\) | ||||
0.561856 | + | 0.827235i | \(0.310087\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.609023 | 0.0755400 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2508 | −1.61884 | −0.809420 | − | 0.587230i | \(-0.800218\pi\) | ||||
−0.809420 | + | 0.587230i | \(0.800218\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.77647 | −1.04158 | −0.520788 | − | 0.853686i | \(-0.674362\pi\) | ||||
−0.520788 | + | 0.853686i | \(0.674362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4182 | −1.45344 | −0.726722 | − | 0.686932i | \(-0.758957\pi\) | ||||
−0.726722 | + | 0.686932i | \(0.758957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.97196 | −0.574113 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.80451 | −0.205643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.52569 | −0.171654 | −0.0858269 | − | 0.996310i | \(-0.527353\pi\) | ||||
−0.0858269 | + | 0.996310i | \(0.527353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7531 | −1.61937 | −0.809683 | − | 0.586867i | \(-0.800361\pi\) | ||||
−0.809683 | + | 0.586867i | \(0.800361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.693141 | −0.0751817 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.77647 | 0.930304 | 0.465152 | − | 0.885231i | \(-0.346000\pi\) | ||||
0.465152 | + | 0.885231i | \(0.346000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63706 | 0.381268 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.195488 | −0.0202712 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.971961 | 0.0997211 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2741 | −1.44932 | −0.724659 | − | 0.689108i | \(-0.758003\pi\) | ||||
−0.724659 | + | 0.689108i | \(0.758003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.80451 | 0.181360 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.63706 | 0.859420 | 0.429710 | − | 0.902967i | \(-0.358616\pi\) | ||||
0.429710 | + | 0.902967i | \(0.358616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.13471 | −0.801537 | −0.400769 | − | 0.916179i | \(-0.631257\pi\) | ||||
−0.400769 | + | 0.916179i | \(0.631257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.167449 | 0.0163414 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.16745 | −0.692903 | −0.346452 | − | 0.938068i | \(-0.612614\pi\) | ||||
−0.346452 | + | 0.938068i | \(0.612614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.44627 | 0.234310 | 0.117155 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117155 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.33490 | −0.316535 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.10668 | 0.480396 | 0.240198 | − | 0.970724i | \(-0.422788\pi\) | ||||
0.240198 | + | 0.970724i | \(0.422788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.167449 | −0.0156147 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.63706 | −0.336247 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.13941 | −0.379459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.74374 | −0.703976 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.94392 | −0.445778 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.66980 | 0.149351 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.97666 | 0.796549 | 0.398275 | − | 0.917266i | \(-0.369609\pi\) | ||||
0.398275 | + | 0.917266i | \(0.369609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.30216 | −0.114649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.86059 | −0.861524 | −0.430762 | − | 0.902466i | \(-0.641755\pi\) | ||||
−0.430762 | + | 0.902466i | \(0.641755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.80451 | 0.503315 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.167449 | −0.0144117 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0000 | −1.11066 | −0.555332 | − | 0.831628i | \(-0.687409\pi\) | ||||
−0.555332 | + | 0.831628i | \(0.687409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3902 | 1.22056 | 0.610280 | − | 0.792186i | \(-0.291057\pi\) | ||||
0.610280 | + | 0.792186i | \(0.291057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.13941 | 0.264386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.56312 | −0.548836 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.837246 | −0.0695295 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.33490 | −0.191282 | −0.0956412 | − | 0.995416i | \(-0.530490\pi\) | ||||
−0.0956412 | + | 0.995416i | \(0.530490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8092 | −0.961020 | −0.480510 | − | 0.876989i | \(-0.659548\pi\) | ||||
−0.480510 | + | 0.876989i | \(0.659548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.13941 | 0.334651 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0327344 | 0.00262929 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.72588 | 0.217549 | 0.108774 | − | 0.994066i | \(-0.465307\pi\) | ||||
0.108774 | + | 0.994066i | \(0.465307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.30686 | 0.262251 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6371 | −1.14646 | −0.573232 | − | 0.819393i | \(-0.694310\pi\) | ||||
−0.573232 | + | 0.819393i | \(0.694310\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.302164 | −0.0235234 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.20018 | −0.0928730 | −0.0464365 | − | 0.998921i | \(-0.514787\pi\) | ||||
−0.0464365 | + | 0.998921i | \(0.514787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.228223 | 0.0175556 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.80451 | −0.443882 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0880 | 1.45124 | 0.725618 | − | 0.688098i | \(-0.241554\pi\) | ||||
0.725618 | + | 0.688098i | \(0.241554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.97196 | 0.375845 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.91588 | 0.369500 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.49765 | −0.560401 | −0.280200 | − | 0.959942i | \(-0.590401\pi\) | ||||
−0.280200 | + | 0.959942i | \(0.590401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4088 | 1.21966 | 0.609830 | − | 0.792532i | \(-0.291238\pi\) | ||||
0.609830 | + | 0.792532i | \(0.291238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.77647 | 0.648776 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.558426 | 0.0410563 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.46961 | 0.546232 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.55294 | 0.112367 | 0.0561836 | − | 0.998420i | \(-0.482107\pi\) | ||||
0.0561836 | + | 0.998420i | \(0.482107\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.1394 | −0.945795 | −0.472898 | − | 0.881117i | \(-0.656792\pi\) | ||||
−0.472898 | + | 0.881117i | \(0.656792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.609023 | 0.0436131 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.8598 | −0.987470 | −0.493735 | − | 0.869612i | \(-0.664369\pi\) | ||||
−0.493735 | + | 0.869612i | \(0.664369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.0600 | −1.35113 | −0.675563 | − | 0.737302i | \(-0.736100\pi\) | ||||
−0.675563 | + | 0.737302i | \(0.736100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2508 | −0.934638 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.827856 | 0.0578199 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4743 | −0.724523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.46961 | 0.514229 | 0.257115 | − | 0.966381i | \(-0.417228\pi\) | ||||
0.257115 | + | 0.966381i | \(0.417228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.77647 | −0.601354 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.218046 | 0.0148706 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.195488 | 0.0132706 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.4182 | −0.839146 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0553 | −1.01273 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.64176 | −0.511730 | −0.255865 | − | 0.966713i | \(-0.582360\pi\) | ||||
−0.255865 | + | 0.966713i | \(0.582360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.97196 | −0.331464 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.1114 | −1.33484 | −0.667419 | − | 0.744682i | \(-0.732601\pi\) | ||||
−0.667419 | + | 0.744682i | \(0.732601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.30686 | 0.482851 | 0.241425 | − | 0.970419i | \(-0.422385\pi\) | ||||
0.241425 | + | 0.970419i | \(0.422385\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.80451 | −0.118728 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.30216 | 0.150820 | 0.0754099 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754099 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.525692 | −0.0342923 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.52569 | −0.0991043 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9767 | −0.774705 | −0.387353 | − | 0.921932i | \(-0.626610\pi\) | ||||
−0.387353 | + | 0.921932i | \(0.626610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.1620 | 1.94290 | 0.971452 | − | 0.237238i | \(-0.0762421\pi\) | ||||
0.971452 | + | 0.237238i | \(0.0762421\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.167449 | −0.0106979 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.1114 | 1.34328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.7531 | −0.934942 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.8606 | −1.19047 | −0.595235 | − | 0.803552i | \(-0.702941\pi\) | ||||
−0.595235 | + | 0.803552i | \(0.702941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.80451 | 0.113449 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.693141 | −0.0434062 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.613718 | −0.0382827 | −0.0191413 | − | 0.999817i | \(-0.506093\pi\) | ||||
−0.0191413 | + | 0.999817i | \(0.506093\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.33490 | 0.207221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.8831 | −1.22605 | −0.613024 | − | 0.790065i | \(-0.710047\pi\) | ||||
−0.613024 | + | 0.790065i | \(0.710047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.553731 | −0.0340154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.77647 | 0.537111 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1020 | 0.798842 | 0.399421 | − | 0.916768i | \(-0.369211\pi\) | ||||
0.399421 | + | 0.916768i | \(0.369211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.53039 | 0.275201 | 0.137601 | − | 0.990488i | \(-0.456061\pi\) | ||||
0.137601 | + | 0.990488i | \(0.456061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.63706 | 0.220125 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.97196 | −0.541030 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22353 | 0.0735147 | 0.0367573 | − | 0.999324i | \(-0.488297\pi\) | ||||
0.0367573 | + | 0.999324i | \(0.488297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.195488 | −0.0117036 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3575 | 0.975804 | 0.487902 | − | 0.872898i | \(-0.337762\pi\) | ||||
0.487902 | + | 0.872898i | \(0.337762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.637062 | −0.0378694 | −0.0189347 | − | 0.999821i | \(-0.506027\pi\) | ||||
−0.0189347 | + | 0.999821i | \(0.506027\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.971961 | 0.0575740 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.94392 | 0.291830 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.134715 | 0.00792440 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2741 | −0.836764 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4969 | 0.788495 | 0.394248 | − | 0.919004i | \(-0.371005\pi\) | ||||
0.394248 | + | 0.919004i | \(0.371005\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.823161 | −0.0479263 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.80451 | 0.104708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.63706 | −0.210337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.30216 | 0.0750555 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.63706 | 0.496186 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.46961 | −0.0841498 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6184 | −1.06261 | −0.531304 | − | 0.847181i | \(-0.678298\pi\) | ||||
−0.531304 | + | 0.847181i | \(0.678298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.13471 | −0.462768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9945 | −1.02038 | −0.510188 | − | 0.860063i | \(-0.670424\pi\) | ||||
−0.510188 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3847 | 1.88702 | 0.943508 | − | 0.331351i | \(-0.107504\pi\) | ||||
0.943508 | + | 0.331351i | \(0.107504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.167449 | 0.00943469 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.77647 | −0.212108 | −0.106054 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106054 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.02256 | 0.505166 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.16745 | −0.400048 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0273 | −1.33691 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.0833 | 1.00308 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.44627 | 0.135279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.13941 | −0.173081 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.60902 | 0.418230 | 0.209115 | − | 0.977891i | \(-0.432942\pi\) | ||||
0.209115 | + | 0.977891i | \(0.432942\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.33490 | −0.182751 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.21883 | 0.121228 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3855 | −1.21942 | −0.609708 | − | 0.792626i | \(-0.708713\pi\) | ||||
−0.609708 | + | 0.792626i | \(0.708713\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.10668 | 0.277357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.352761 | −0.0191031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.167449 | −0.00901516 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.4922 | −1.36849 | −0.684246 | − | 0.729252i | \(-0.739868\pi\) | ||||
−0.684246 | + | 0.729252i | \(0.739868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1900 | 0.545459 | 0.272729 | − | 0.962091i | \(-0.412074\pi\) | ||||
0.272729 | + | 0.962091i | \(0.412074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.63706 | −0.194132 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2134 | 1.02262 | 0.511312 | − | 0.859395i | \(-0.329160\pi\) | ||||
0.511312 | + | 0.859395i | \(0.329160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46961 | 0.0779990 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.13941 | −0.219081 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.11607 | −0.0589037 | −0.0294519 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294519 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6924 | 0.773282 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.74374 | −0.406441 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.07942 | 0.108842 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.69314 | −0.297180 | −0.148590 | − | 0.988899i | \(-0.547473\pi\) | ||||
−0.148590 | + | 0.988899i | \(0.547473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.94392 | −0.257370 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.30686 | −0.171684 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.2967 | −1.46515 | −0.732573 | − | 0.680688i | \(-0.761681\pi\) | ||||
−0.732573 | + | 0.680688i | \(0.761681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.66980 | 0.0862279 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.1853 | −0.936591 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3622 | −0.686368 | −0.343184 | − | 0.939268i | \(-0.611505\pi\) | ||||
−0.343184 | + | 0.939268i | \(0.611505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.97666 | 0.459888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.75313 | 0.140678 | 0.0703391 | − | 0.997523i | \(-0.477592\pi\) | ||||
0.0703391 | + | 0.997523i | \(0.477592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.302164 | 0.0153997 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.30216 | −0.0661927 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.92136 | 0.350927 | 0.175464 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175464 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.13941 | 0.209339 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.86059 | −0.497401 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.255476 | 0.0128544 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.60433 | −0.130707 | −0.0653537 | − | 0.997862i | \(-0.520818\pi\) | ||||
−0.0653537 | + | 0.997862i | \(0.520818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.80451 | 0.290589 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.13941 | −0.106837 | −0.0534185 | − | 0.998572i | \(-0.517012\pi\) | ||||
−0.0534185 | + | 0.998572i | \(0.517012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.711004 | 0.0354176 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.167449 | −0.00832062 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.01786 | −0.298294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.2500 | −1.69355 | −0.846777 | − | 0.531949i | \(-0.821460\pi\) | ||||
−0.846777 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.0000 | −0.641243 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.91588 | −0.241895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.47040 | 0.121267 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3902 | 0.704691 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.91119 | −0.191074 | −0.0955370 | − | 0.995426i | \(-0.530457\pi\) | ||||
−0.0955370 | + | 0.995426i | \(0.530457\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.5249 | −1.53643 | −0.768215 | − | 0.640192i | \(-0.778855\pi\) | ||||
−0.768215 | + | 0.640192i | \(0.778855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.13941 | 0.152643 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.5810 | −0.998324 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.77647 | −0.424723 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.56312 | −0.316870 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5716 | 0.942730 | 0.471365 | − | 0.881938i | \(-0.343761\pi\) | ||||
0.471365 | + | 0.881938i | \(0.343761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0880 | −0.773141 | −0.386571 | − | 0.922260i | \(-0.626340\pi\) | ||||
−0.386571 | + | 0.922260i | \(0.626340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.837246 | −0.0401429 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.80451 | −0.277667 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0833 | −0.958525 | −0.479263 | − | 0.877672i | \(-0.659096\pi\) | ||||
−0.479263 | + | 0.877672i | \(0.659096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0833 | 0.526585 | 0.263292 | − | 0.964716i | \(-0.415192\pi\) | ||||
0.263292 | + | 0.964716i | \(0.415192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.46961 | −0.0696663 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.33490 | −0.110437 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.8598 | −1.45636 | −0.728182 | − | 0.685384i | \(-0.759634\pi\) | ||||
−0.728182 | + | 0.685384i | \(0.759634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.92136 | −0.420091 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8092 | −0.554845 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.609023 | −0.0285514 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.91588 | 0.323511 | 0.161756 | − | 0.986831i | \(-0.448284\pi\) | ||||
0.161756 | + | 0.986831i | \(0.448284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.13941 | 0.193211 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.4688 | −1.41907 | −0.709537 | − | 0.704668i | \(-0.751096\pi\) | ||||
−0.709537 | + | 0.704668i | \(0.751096\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.9392 | 1.39139 | 0.695697 | − | 0.718335i | \(-0.255096\pi\) | ||||
0.695697 | + | 0.718335i | \(0.255096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0327344 | 0.00151802 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.21805 | 0.287737 | 0.143868 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143868 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2508 | 0.611864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.72588 | 0.125602 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.34977 | −0.108043 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8598 | 1.32418 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.30686 | 0.151411 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −43.6457 | −1.99422 | −0.997111 | − | 0.0759622i | \(-0.975797\pi\) | ||||
−0.997111 | + | 0.0759622i | \(0.975797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1292 | 0.553045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.39019 | 0.108533 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1059 | 1.18297 | 0.591485 | − | 0.806316i | \(-0.298542\pi\) | ||||
0.591485 | + | 0.806316i | \(0.298542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.6371 | −0.661911 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.99921 | 0.225611 | 0.112806 | − | 0.993617i | \(-0.464016\pi\) | ||||
0.112806 | + | 0.993617i | \(0.464016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.6970 | 0.932148 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.302164 | −0.0135813 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.77647 | 0.393679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2508 | 1.21991 | 0.609956 | − | 0.792435i | \(-0.291187\pi\) | ||||
0.609956 | + | 0.792435i | \(0.291187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.20018 | −0.0536202 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4174 | 1.75754 | 0.878768 | − | 0.477248i | \(-0.158366\pi\) | ||||
0.878768 | + | 0.477248i | \(0.158366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.44627 | −0.0643581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.228223 | 0.0101357 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.7710 | −1.62985 | −0.814923 | − | 0.579570i | \(-0.803221\pi\) | ||||
−0.814923 | + | 0.579570i | \(0.803221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4182 | 0.549350 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.80451 | −0.256275 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.36215 | 0.0600236 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.66510 | 0.249151 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.0880 | 0.837871 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.8878 | 0.958924 | 0.479462 | − | 0.877563i | \(-0.340832\pi\) | ||||
0.479462 | + | 0.877563i | \(0.340832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2180 | 0.752893 | 0.376446 | − | 0.926438i | \(-0.377146\pi\) | ||||
0.376446 | + | 0.926438i | \(0.377146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.97196 | 0.216994 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.809207 | −0.0352496 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.91588 | 0.213331 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.9814 | 0.778859 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.20018 | 0.0518885 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.49765 | −0.323548 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.80451 | 0.0777258 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6745 | −1.01785 | −0.508923 | − | 0.860812i | \(-0.669956\pi\) | ||||
−0.508923 | + | 0.860812i | \(0.669956\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.4088 | 0.704171 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.409626 | −0.0175464 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.9206 | 1.70688 | 0.853440 | − | 0.521191i | \(-0.174512\pi\) | ||||
0.853440 | + | 0.521191i | \(0.174512\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.77647 | 0.374571 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.0226 | −1.23640 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.52569 | 0.0648790 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.558426 | 0.0237039 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2835 | 0.986554 | 0.493277 | − | 0.869872i | \(-0.335799\pi\) | ||||
0.493277 | + | 0.869872i | \(0.335799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.73605 | 0.200314 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.46961 | 0.315367 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4735 | 1.36860 | 0.684298 | − | 0.729203i | \(-0.260109\pi\) | ||||
0.684298 | + | 0.729203i | \(0.260109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.855109 | −0.0359747 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1441 | −0.592952 | −0.296476 | − | 0.955040i | \(-0.595811\pi\) | ||||
−0.296476 | + | 0.955040i | \(0.595811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3715 | −1.35471 | −0.677353 | − | 0.735658i | \(-0.736873\pi\) | ||||
−0.677353 | + | 0.735658i | \(0.736873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.55294 | 0.0648752 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.97196 | −0.207345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7757 | −0.573489 | −0.286745 | − | 0.958007i | \(-0.592573\pi\) | ||||
−0.286745 | + | 0.958007i | \(0.592573\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1394 | −0.546055 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7531 | 0.612063 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.96727 | 0.247139 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.609023 | 0.0251800 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.1721 | 0.915142 | 0.457571 | − | 0.889173i | \(-0.348719\pi\) | ||||
0.457571 | + | 0.889173i | \(0.348719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.13471 | 0.0467551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.8598 | −0.570116 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.3668 | 1.08276 | 0.541378 | − | 0.840779i | \(-0.317903\pi\) | ||||
0.541378 | + | 0.840779i | \(0.317903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.693141 | 0.0284160 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.0600 | −0.780073 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.89332 | 0.0773591 | 0.0386796 | − | 0.999252i | \(-0.487685\pi\) | ||||
0.0386796 | + | 0.999252i | \(0.487685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.96257 | −0.120846 | −0.0604229 | − | 0.998173i | \(-0.519245\pi\) | ||||
−0.0604229 | + | 0.998173i | \(0.519245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2508 | −0.539614 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.29668 | 0.0527176 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.67058 | 0.0678069 | 0.0339034 | − | 0.999425i | \(-0.489206\pi\) | ||||
0.0339034 | + | 0.999425i | \(0.489206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | −0.202610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.4182 | −0.461932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.1059 | −0.569732 | −0.284866 | − | 0.958567i | \(-0.591949\pi\) | ||||
−0.284866 | + | 0.958567i | \(0.591949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.827856 | 0.0333824 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4510 | 0.501257 | 0.250628 | − | 0.968083i | \(-0.419363\pi\) | ||||
0.250628 | + | 0.968083i | \(0.419363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.9945 | −0.642874 | −0.321437 | − | 0.946931i | \(-0.604166\pi\) | ||||
−0.321437 | + | 0.946931i | \(0.604166\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.77647 | −0.351622 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5802 | 0.983208 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4743 | −0.418304 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.8045 | −0.550422 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.6970 | −1.77936 | −0.889681 | − | 0.456583i | \(-0.849073\pi\) | ||||
−0.889681 | + | 0.456583i | \(0.849073\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.46961 | 0.296890 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.50313 | −0.0596500 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.63706 | −0.144106 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.77647 | −0.347192 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.37233 | −0.251692 | −0.125846 | − | 0.992050i | \(-0.540164\pi\) | ||||
−0.125846 | + | 0.992050i | \(0.540164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.11607 | −0.0834495 | −0.0417247 | − | 0.999129i | \(-0.513285\pi\) | ||||
−0.0417247 | + | 0.999129i | \(0.513285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.218046 | 0.00858557 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.98135 | −0.274465 | −0.137233 | − | 0.990539i | \(-0.543821\pi\) | ||||
−0.137233 | + | 0.990539i | \(0.543821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.87077 | 0.348208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.195488 | 0.00766180 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.5522 | 1.86086 | 0.930430 | − | 0.366470i | \(-0.119434\pi\) | ||||
0.930430 | + | 0.366470i | \(0.119434\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.65115 | 0.0645157 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4182 | −0.484481 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.5708 | 1.54146 | 0.770730 | − | 0.637162i | \(-0.219892\pi\) | ||||
0.770730 | + | 0.637162i | \(0.219892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.4088 | 1.26056 | 0.630279 | − | 0.776369i | \(-0.282941\pi\) | ||||
0.630279 | + | 0.776369i | \(0.282941\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.0553 | −0.584699 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.971961 | −0.0376910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.64176 | −0.295447 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.8372 | 0.611390 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.05138 | −0.310358 | −0.155179 | − | 0.987886i | \(-0.549595\pi\) | ||||
−0.155179 | + | 0.987886i | \(0.549595\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.97196 | −0.191371 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.0647 | −0.578983 | −0.289491 | − | 0.957181i | \(-0.593486\pi\) | ||||
−0.289491 | + | 0.957181i | \(0.593486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.2741 | 0.547791 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.1114 | −0.770669 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.3481 | −1.27603 | −0.638014 | − | 0.770025i | \(-0.720244\pi\) | ||||
−0.638014 | + | 0.770025i | \(0.720244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.17684 | 0.0831728 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.30686 | 0.278774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0273 | −0.458202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1853 | 0.920053 | 0.460026 | − | 0.887905i | \(-0.347840\pi\) | ||||
0.460026 | + | 0.887905i | \(0.347840\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.80451 | −0.0685477 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.40963 | −0.0914023 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.4649 | −0.775164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.30216 | 0.0870758 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.69314 | 0.328335 | 0.164168 | − | 0.986432i | \(-0.447506\pi\) | ||||
0.164168 | + | 0.986432i | \(0.447506\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.3575 | 0.730080 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.525692 | −0.0197987 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.63706 | −0.324830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0973 | −0.529435 | −0.264717 | − | 0.964326i | \(-0.585279\pi\) | ||||
−0.264717 | + | 0.964326i | \(0.585279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.52569 | −0.0572179 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.195488 | −0.00732110 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.09899 | 0.0410999 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.9767 | −0.447276 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.0607736 | 0.00226647 | 0.00113324 | − | 0.999999i | \(-0.499639\pi\) | ||||
0.00113324 | + | 0.999999i | \(0.499639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.13471 | 0.302953 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.1620 | 1.12174 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.8598 | −0.923270 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.743738 | −0.0275837 | −0.0137919 | − | 0.999905i | \(-0.504390\pi\) | ||||
−0.0137919 | + | 0.999905i | \(0.504390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.39019 | −0.199363 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.6043 | −1.35201 | −0.676006 | − | 0.736896i | \(-0.736291\pi\) | ||||
−0.676006 | + | 0.736896i | \(0.736291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.167449 | −0.00617646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.9112 | −0.880780 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.8606 | 0.509870 | 0.254935 | − | 0.966958i | \(-0.417946\pi\) | ||||
0.254935 | + | 0.966958i | \(0.417946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.1114 | 0.775546 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.96727 | 0.218918 | 0.109459 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109459 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.390977 | 0.0143243 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7531 | −0.539789 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.16745 | 0.261893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.19627 | 0.189615 | 0.0948074 | − | 0.995496i | \(-0.469776\pi\) | ||||
0.0948074 | + | 0.995496i | \(0.469776\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.8606 | −0.687318 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.97744 | 0.0719665 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.4088 | 0.596389 | 0.298195 | − | 0.954505i | \(-0.403616\pi\) | ||||
0.298195 | + | 0.954505i | \(0.403616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.80451 | 0.0654996 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.2882 | 0.735447 | 0.367724 | − | 0.929935i | \(-0.380137\pi\) | ||||
0.367724 | + | 0.929935i | \(0.380137\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.44627 | −0.0885609 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.693141 | −0.0250606 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.8794 | −0.645587 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.92136 | −0.357774 | −0.178887 | − | 0.983870i | \(-0.557250\pi\) | ||||
−0.178887 | + | 0.983870i | \(0.557250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.613718 | −0.0221025 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.7055 | −1.64391 | −0.821957 | − | 0.569550i | \(-0.807117\pi\) | ||||
−0.821957 | + | 0.569550i | \(0.807117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.971961 | 0.0349139 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.33490 | 0.119639 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.6970 | 1.02818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8372 | −0.566701 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.456446 | −0.0162912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.8084 | 1.34772 | 0.673862 | − | 0.738857i | \(-0.264634\pi\) | ||||
0.673862 | + | 0.738857i | \(0.264634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8831 | −0.707859 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.10668 | −0.181572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.9206 | −1.13353 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.553731 | −0.0196388 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.9151 | 0.386633 | 0.193316 | − | 0.981136i | \(-0.438076\pi\) | ||||
0.193316 | + | 0.981136i | \(0.438076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9953 | 0.459741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.77647 | 0.310101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.4088 | −0.790791 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.167449 | 0.00590181 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1020 | 0.461212 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.2733 | 0.501824 | 0.250912 | − | 0.968010i | \(-0.419270\pi\) | ||||
0.250912 | + | 0.968010i | \(0.419270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7804 | 1.53734 | 0.768669 | − | 0.639647i | \(-0.220920\pi\) | ||||
0.768669 | + | 0.639647i | \(0.220920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.53039 | 0.158888 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.45096 | 0.0858535 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.55843 | 0.264436 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.63706 | 0.127089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1620 | 1.08756 | 0.543780 | − | 0.839228i | \(-0.316993\pi\) | ||||
0.543780 | + | 0.839228i | \(0.316993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7859 | −0.550261 | −0.275130 | − | 0.961407i | \(-0.588721\pi\) | ||||
−0.275130 | + | 0.961407i | \(0.588721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.97196 | −0.312364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.3661 | −1.40367 | −0.701833 | − | 0.712342i | \(-0.747635\pi\) | ||||
−0.701833 | + | 0.712342i | \(0.747635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.42293 | 0.327272 | 0.163636 | − | 0.986521i | \(-0.447678\pi\) | ||||
0.163636 | + | 0.986521i | \(0.447678\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.22353 | 0.0424437 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.13941 | 0.143422 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.200970 | 0.00695485 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.195488 | −0.00675707 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.83725 | −0.201524 | −0.100762 | − | 0.994911i | \(-0.532128\pi\) | ||||
−0.100762 | + | 0.994911i | \(0.532128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.3575 | 0.563381 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0382157 | −0.00131466 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.74374 | 0.266078 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.637062 | −0.0218639 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.33490 | −0.114319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9120 | 0.407858 | 0.203929 | − | 0.978986i | \(-0.434629\pi\) | ||||
0.203929 | + | 0.978986i | \(0.434629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.971961 | 0.0332404 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6970 | 0.604520 | 0.302260 | − | 0.953226i | \(-0.402259\pi\) | ||||
0.302260 | + | 0.953226i | \(0.402259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6924 | 0.774253 | 0.387127 | − | 0.922027i | \(-0.373468\pi\) | ||||
0.387127 | + | 0.922027i | \(0.373468\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.94392 | 0.168488 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.8412 | 0.675401 | 0.337700 | − | 0.941254i | \(-0.390351\pi\) | ||||
0.337700 | + | 0.941254i | \(0.390351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.19627 | −0.108677 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.134715 | 0.00457515 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.75313 | −0.0933935 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.1939 | 1.63299 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.2741 | −0.483106 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.66980 | −0.0564494 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.0965 | −1.11759 | −0.558795 | − | 0.829306i | \(-0.688736\pi\) | ||||
−0.558795 | + | 0.829306i | \(0.688736\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.4969 | 0.455238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2134 | −1.55697 | −0.778484 | − | 0.627665i | \(-0.784011\pi\) | ||||
−0.778484 | + | 0.627665i | \(0.784011\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.7671 | 0.362341 | 0.181171 | − | 0.983452i | \(-0.442011\pi\) | ||||
0.181171 | + | 0.983452i | \(0.442011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.823161 | −0.0276702 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.3153 | −1.18577 | −0.592886 | − | 0.805286i | \(-0.702012\pi\) | ||||
−0.592886 | + | 0.805286i | \(0.702012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.97666 | −0.301067 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.80451 | 0.0604534 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.2227 | −0.609801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.25548 | 0.0419659 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.63706 | −0.121438 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.977442 | −0.0325995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6884 | 0.456028 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.30216 | 0.0433333 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.74765 | −0.0913349 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7157 | 0.887080 | 0.443540 | − | 0.896255i | \(-0.353722\pi\) | ||||
0.443540 | + | 0.896255i | \(0.353722\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.63706 | 0.286473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2453 | 0.471968 | 0.235984 | − | 0.971757i | \(-0.424169\pi\) | ||||
0.235984 | + | 0.971757i | \(0.424169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.6222 | −0.881066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.46961 | −0.0485839 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.86059 | 0.325625 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.20018 | 0.303486 | 0.151743 | − | 0.988420i | \(-0.451511\pi\) | ||||
0.151743 | + | 0.988420i | \(0.451511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.6184 | −0.613498 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.9206 | 1.05068 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.5810 | 0.545179 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.13471 | −0.267179 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.4416 | −0.900329 | −0.450164 | − | 0.892946i | \(-0.648635\pi\) | ||||
−0.450164 | + | 0.892946i | \(0.648635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.80451 | −0.190235 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.9945 | −0.589114 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.25078 | −0.0409049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.8785 | 0.682069 | 0.341035 | − | 0.940051i | \(-0.389223\pi\) | ||||
0.341035 | + | 0.940051i | \(0.389223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.3847 | 1.08947 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2469 | 0.790425 | 0.395213 | − | 0.918590i | \(-0.370671\pi\) | ||||
0.395213 | + | 0.918590i | \(0.370671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.94392 | −0.160996 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.167449 | 0.00544712 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.41353 | −0.143421 | −0.0717103 | − | 0.997426i | \(-0.522846\pi\) | ||||
−0.0717103 | + | 0.997426i | \(0.522846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.1659 | 1.46615 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.77647 | −0.122461 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.21883 | −0.266234 | −0.133117 | − | 0.991100i | \(-0.542499\pi\) | ||||
−0.133117 | + | 0.991100i | \(0.542499\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.260039 | −0.00841468 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.02256 | 0.291658 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.0000 | 0.419792 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9618 | −0.998767 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.16745 | −0.230968 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.20018 | 0.0708264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.48748 | −0.176465 | −0.0882327 | − | 0.996100i | \(-0.528122\pi\) | ||||
−0.0882327 | + | 0.996100i | \(0.528122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0273 | −0.771867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.2686 | −1.64529 | −0.822645 | − | 0.568556i | \(-0.807502\pi\) | ||||
−0.822645 | + | 0.568556i | \(0.807502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3902 | −0.461328 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0833 | 0.579130 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.25548 | 0.104152 | 0.0520759 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520759 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.8372 | 0.506161 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.44627 | 0.0781034 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.03195 | 0.288074 | 0.144037 | − | 0.989572i | \(-0.453992\pi\) | ||||
0.144037 | + | 0.989572i | \(0.453992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.32081 | 0.0739472 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.13941 | −0.0999285 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.30216 | −0.0414064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.4510 | −1.34850 | −0.674250 | − | 0.738503i | \(-0.735533\pi\) | ||||
−0.674250 | + | 0.738503i | \(0.735533\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.60902 | 0.241465 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.19158 | 0.101180 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.6222 | 1.28652 | 0.643259 | − | 0.765649i | \(-0.277582\pi\) | ||||
0.643259 | + | 0.765649i | \(0.277582\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.33490 | −0.105512 |
(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 | 7728.2.a.bx.1.2 | 3 | ||
4.3 | odd | 2 | 3864.2.a.m.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.m.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
7728.2.a.bx.1.2 | 3 | 1.1 | even | 1 | trivial |