Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.13366265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1875) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.52260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52260 | 1.07664 | 0.538320 | − | 0.842740i | \(-0.319059\pi\) | ||||
0.538320 | + | 0.842740i | \(0.319059\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.318310 | 0.159155 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.990985 | −0.374557 | −0.187279 | − | 0.982307i | \(-0.559967\pi\) | ||||
−0.187279 | + | 0.982307i | \(0.559967\pi\) | |||||||
\(8\) | −2.56054 | −0.905288 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.97349 | −1.80107 | −0.900537 | − | 0.434779i | \(-0.856826\pi\) | ||||
−0.900537 | + | 0.434779i | \(0.856826\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.02992 | 1.11770 | 0.558850 | − | 0.829269i | \(-0.311243\pi\) | ||||
0.558850 | + | 0.829269i | \(0.311243\pi\) | |||||||
\(14\) | −1.50887 | −0.403263 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.53530 | −1.13382 | ||||||||
\(17\) | −0.476176 | −0.115490 | −0.0577448 | − | 0.998331i | \(-0.518391\pi\) | ||||
−0.0577448 | + | 0.998331i | \(0.518391\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82322 | 0.647692 | 0.323846 | − | 0.946110i | \(-0.395024\pi\) | ||||
0.323846 | + | 0.946110i | \(0.395024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.09523 | −1.93911 | ||||||||
\(23\) | 1.74696 | 0.364267 | 0.182134 | − | 0.983274i | \(-0.441700\pi\) | ||||
0.182134 | + | 0.983274i | \(0.441700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.13596 | 1.20336 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.315440 | −0.0596127 | ||||||||
\(29\) | 1.41641 | 0.263020 | 0.131510 | − | 0.991315i | \(-0.458017\pi\) | ||||
0.131510 | + | 0.991315i | \(0.458017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.76141 | 1.57360 | 0.786798 | − | 0.617211i | \(-0.211737\pi\) | ||||
0.786798 | + | 0.617211i | \(0.211737\pi\) | |||||||
\(32\) | −1.78436 | −0.315434 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.725025 | −0.124341 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.06031 | −1.32511 | −0.662553 | − | 0.749015i | \(-0.730527\pi\) | ||||
−0.662553 | + | 0.749015i | \(0.730527\pi\) | |||||||
\(38\) | 4.29864 | 0.697332 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.50296 | 0.859418 | 0.429709 | − | 0.902967i | \(-0.358616\pi\) | ||||
0.429709 | + | 0.902967i | \(0.358616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.82255 | −1.04043 | −0.520214 | − | 0.854036i | \(-0.674148\pi\) | ||||
−0.520214 | + | 0.854036i | \(0.674148\pi\) | |||||||
\(44\) | −1.90142 | −0.286650 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.65993 | 0.392185 | ||||||||
\(47\) | 9.62845 | 1.40445 | 0.702227 | − | 0.711953i | \(-0.252189\pi\) | ||||
0.702227 | + | 0.711953i | \(0.252189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.01795 | −0.859707 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.28276 | 0.177887 | ||||||||
\(53\) | −6.57994 | −0.903824 | −0.451912 | − | 0.892063i | \(-0.649258\pi\) | ||||
−0.451912 | + | 0.892063i | \(0.649258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.53746 | 0.339082 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.15662 | 0.283179 | ||||||||
\(59\) | −13.0760 | −1.70235 | −0.851177 | − | 0.524879i | \(-0.824111\pi\) | ||||
−0.851177 | + | 0.524879i | \(0.824111\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2013 | 1.56222 | 0.781108 | − | 0.624397i | \(-0.214655\pi\) | ||||
0.781108 | + | 0.624397i | \(0.214655\pi\) | |||||||
\(62\) | 13.3401 | 1.69420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.35373 | 0.794216 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3195 | 1.38289 | 0.691445 | − | 0.722429i | \(-0.256974\pi\) | ||||
0.691445 | + | 0.722429i | \(0.256974\pi\) | |||||||
\(68\) | −0.151571 | −0.0183807 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.43047 | 0.644478 | 0.322239 | − | 0.946658i | \(-0.395564\pi\) | ||||
0.322239 | + | 0.946658i | \(0.395564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.08935 | −0.478622 | −0.239311 | − | 0.970943i | \(-0.576922\pi\) | ||||
−0.239311 | + | 0.970943i | \(0.576922\pi\) | |||||||
\(74\) | −12.2726 | −1.42666 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.898661 | 0.103083 | ||||||||
\(77\) | 5.91964 | 0.674605 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0070 | 1.68842 | 0.844212 | − | 0.536009i | \(-0.180069\pi\) | ||||
0.844212 | + | 0.536009i | \(0.180069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.37881 | 0.925284 | ||||||||
\(83\) | 2.29898 | 0.252346 | 0.126173 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126173 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3880 | −1.12017 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 15.2954 | 1.63049 | ||||||||
\(89\) | −6.26920 | −0.664533 | −0.332267 | − | 0.943185i | \(-0.607813\pi\) | ||||
−0.332267 | + | 0.943185i | \(0.607813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.99359 | −0.418642 | ||||||||
\(92\) | 0.556076 | 0.0579749 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.6603 | 1.51209 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2541 | 1.34575 | 0.672875 | − | 0.739756i | \(-0.265059\pi\) | ||||
0.672875 | + | 0.739756i | \(0.265059\pi\) | |||||||
\(98\) | −9.16293 | −0.925595 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.41452 | 0.638269 | 0.319134 | − | 0.947709i | \(-0.396608\pi\) | ||||
0.319134 | + | 0.947709i | \(0.396608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.38309 | 0.924543 | 0.462272 | − | 0.886738i | \(-0.347034\pi\) | ||||
0.462272 | + | 0.886738i | \(0.347034\pi\) | |||||||
\(104\) | −10.3188 | −1.01184 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0186 | −0.973094 | ||||||||
\(107\) | 13.4108 | 1.29647 | 0.648234 | − | 0.761441i | \(-0.275508\pi\) | ||||
0.648234 | + | 0.761441i | \(0.275508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.81573 | 0.269698 | 0.134849 | − | 0.990866i | \(-0.456945\pi\) | ||||
0.134849 | + | 0.990866i | \(0.456945\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.49441 | 0.424682 | ||||||||
\(113\) | 19.4252 | 1.82737 | 0.913685 | − | 0.406423i | \(-0.133224\pi\) | ||||
0.913685 | + | 0.406423i | \(0.133224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.450857 | 0.0418610 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.9096 | −1.83282 | ||||||||
\(119\) | 0.471883 | 0.0432574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.6825 | 2.24387 | ||||||||
\(122\) | 18.5777 | 1.68194 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.78884 | 0.250446 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.42366 | 0.570008 | 0.285004 | − | 0.958526i | \(-0.408005\pi\) | ||||
0.285004 | + | 0.958526i | \(0.408005\pi\) | |||||||
\(128\) | 13.2429 | 1.17052 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30057 | 0.637853 | 0.318927 | − | 0.947779i | \(-0.396678\pi\) | ||||
0.318927 | + | 0.947779i | \(0.396678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.79777 | −0.242598 | ||||||||
\(134\) | 17.2350 | 1.48888 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.21927 | 0.104551 | ||||||||
\(137\) | 7.84860 | 0.670552 | 0.335276 | − | 0.942120i | \(-0.391171\pi\) | ||||
0.335276 | + | 0.942120i | \(0.391171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0514 | −1.44628 | −0.723138 | − | 0.690703i | \(-0.757301\pi\) | ||||
−0.723138 | + | 0.690703i | \(0.757301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.26844 | 0.693872 | ||||||||
\(143\) | −24.0727 | −2.01306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.22644 | −0.515304 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.56568 | −0.210897 | ||||||||
\(149\) | −2.84365 | −0.232961 | −0.116480 | − | 0.993193i | \(-0.537161\pi\) | ||||
−0.116480 | + | 0.993193i | \(0.537161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5744 | 0.941915 | 0.470958 | − | 0.882156i | \(-0.343908\pi\) | ||||
0.470958 | + | 0.882156i | \(0.343908\pi\) | |||||||
\(152\) | −7.22898 | −0.586348 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.01324 | 0.726307 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.77270 | 0.380903 | 0.190452 | − | 0.981697i | \(-0.439005\pi\) | ||||
0.190452 | + | 0.981697i | \(0.439005\pi\) | |||||||
\(158\) | 22.8497 | 1.81783 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.73122 | −0.136439 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.98657 | 0.233926 | 0.116963 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116963 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(164\) | 1.75165 | 0.136781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50043 | 0.271686 | ||||||||
\(167\) | −18.6105 | −1.44012 | −0.720060 | − | 0.693912i | \(-0.755886\pi\) | ||||
−0.720060 | + | 0.693912i | \(0.755886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.24028 | 0.249252 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.17169 | −0.165589 | ||||||||
\(173\) | −16.3578 | −1.24366 | −0.621829 | − | 0.783153i | \(-0.713610\pi\) | ||||
−0.621829 | + | 0.783153i | \(0.713610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27.0915 | 2.04210 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.54548 | −0.715464 | ||||||||
\(179\) | 15.2266 | 1.13809 | 0.569045 | − | 0.822307i | \(-0.307313\pi\) | ||||
0.569045 | + | 0.822307i | \(0.307313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.44321 | −0.255932 | −0.127966 | − | 0.991779i | \(-0.540845\pi\) | ||||
−0.127966 | + | 0.991779i | \(0.540845\pi\) | |||||||
\(182\) | −6.08064 | −0.450727 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.47317 | −0.329767 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.84443 | 0.208005 | ||||||||
\(188\) | 3.06483 | 0.223526 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1752 | −1.09804 | −0.549020 | − | 0.835809i | \(-0.684999\pi\) | ||||
−0.549020 | + | 0.835809i | \(0.684999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0304 | 1.00993 | 0.504965 | − | 0.863140i | \(-0.331505\pi\) | ||||
0.504965 | + | 0.863140i | \(0.331505\pi\) | |||||||
\(194\) | 20.1807 | 1.44889 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.91557 | −0.136827 | ||||||||
\(197\) | −23.7871 | −1.69476 | −0.847382 | − | 0.530984i | \(-0.821823\pi\) | ||||
−0.847382 | + | 0.530984i | \(0.821823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9445 | −1.13028 | −0.565139 | − | 0.824996i | \(-0.691177\pi\) | ||||
−0.565139 | + | 0.824996i | \(0.691177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.76675 | 0.687186 | ||||||||
\(203\) | −1.40364 | −0.0985162 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.2867 | 0.995401 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.2769 | −1.26728 | ||||||||
\(209\) | −16.8645 | −1.16654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.49016 | −0.446801 | −0.223401 | − | 0.974727i | \(-0.571716\pi\) | ||||
−0.223401 | + | 0.974727i | \(0.571716\pi\) | |||||||
\(212\) | −2.09446 | −0.143848 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.4192 | 1.39583 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.68243 | −0.589402 | ||||||||
\(218\) | 4.28723 | 0.290368 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.91895 | −0.129083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.7454 | 0.719562 | 0.359781 | − | 0.933037i | \(-0.382851\pi\) | ||||
0.359781 | + | 0.933037i | \(0.382851\pi\) | |||||||
\(224\) | 1.76828 | 0.118148 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 29.5768 | 1.96742 | ||||||||
\(227\) | 6.84922 | 0.454599 | 0.227299 | − | 0.973825i | \(-0.427010\pi\) | ||||
0.227299 | + | 0.973825i | \(0.427010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.21379 | 0.146291 | 0.0731457 | − | 0.997321i | \(-0.476696\pi\) | ||||
0.0731457 | + | 0.997321i | \(0.476696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.62677 | −0.238109 | ||||||||
\(233\) | 9.39682 | 0.615606 | 0.307803 | − | 0.951450i | \(-0.400406\pi\) | ||||
0.307803 | + | 0.951450i | \(0.400406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.16223 | −0.270938 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.718489 | 0.0465727 | ||||||||
\(239\) | 0.737315 | 0.0476930 | 0.0238465 | − | 0.999716i | \(-0.492409\pi\) | ||||
0.0238465 | + | 0.999716i | \(0.492409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.21895 | −0.271767 | −0.135883 | − | 0.990725i | \(-0.543387\pi\) | ||||
−0.135883 | + | 0.990725i | \(0.543387\pi\) | |||||||
\(242\) | 37.5816 | 2.41584 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.88379 | 0.248634 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3774 | 0.723925 | ||||||||
\(248\) | −22.4339 | −1.42456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.82121 | 0.619909 | 0.309955 | − | 0.950751i | \(-0.399686\pi\) | ||||
0.309955 | + | 0.950751i | \(0.399686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4355 | −0.656072 | ||||||||
\(254\) | 9.78067 | 0.613694 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.45620 | 0.466012 | ||||||||
\(257\) | −0.0383881 | −0.00239458 | −0.00119729 | − | 0.999999i | \(-0.500381\pi\) | ||||
−0.00119729 | + | 0.999999i | \(0.500381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98764 | 0.496328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.1158 | 0.686739 | ||||||||
\(263\) | 14.2706 | 0.879965 | 0.439982 | − | 0.898006i | \(-0.354985\pi\) | ||||
0.439982 | + | 0.898006i | \(0.354985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.25989 | −0.261191 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.60309 | 0.220094 | ||||||||
\(269\) | −21.4090 | −1.30533 | −0.652666 | − | 0.757646i | \(-0.726349\pi\) | ||||
−0.652666 | + | 0.757646i | \(0.726349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.22804 | 0.378327 | 0.189163 | − | 0.981946i | \(-0.439422\pi\) | ||||
0.189163 | + | 0.981946i | \(0.439422\pi\) | |||||||
\(272\) | 2.15960 | 0.130945 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9503 | 0.721943 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0431 | −0.843768 | −0.421884 | − | 0.906650i | \(-0.638631\pi\) | ||||
−0.421884 | + | 0.906650i | \(0.638631\pi\) | |||||||
\(278\) | −25.9624 | −1.55712 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.516993 | 0.0308412 | 0.0154206 | − | 0.999881i | \(-0.495091\pi\) | ||||
0.0154206 | + | 0.999881i | \(0.495091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.977154 | 0.0580858 | 0.0290429 | − | 0.999578i | \(-0.490754\pi\) | ||||
0.0290429 | + | 0.999578i | \(0.490754\pi\) | |||||||
\(284\) | 1.72857 | 0.102572 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −36.6531 | −2.16734 | ||||||||
\(287\) | −5.45335 | −0.321901 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7733 | −0.986662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.30168 | −0.0761751 | ||||||||
\(293\) | −2.75561 | −0.160984 | −0.0804922 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804922 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 20.6387 | 1.19960 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.32974 | −0.250815 | ||||||||
\(299\) | 7.04013 | 0.407141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.76104 | 0.389700 | ||||||||
\(302\) | 17.6233 | 1.01410 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.8042 | −0.734369 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1940 | 0.924241 | 0.462120 | − | 0.886817i | \(-0.347089\pi\) | ||||
0.462120 | + | 0.886817i | \(0.347089\pi\) | |||||||
\(308\) | 1.88428 | 0.107367 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.20094 | −0.465033 | −0.232516 | − | 0.972593i | \(-0.574696\pi\) | ||||
−0.232516 | + | 0.972593i | \(0.574696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0065 | 1.13083 | 0.565416 | − | 0.824806i | \(-0.308716\pi\) | ||||
0.565416 | + | 0.824806i | \(0.308716\pi\) | |||||||
\(314\) | 7.26691 | 0.410096 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.77689 | 0.268721 | ||||||||
\(317\) | 6.52708 | 0.366597 | 0.183299 | − | 0.983057i | \(-0.441322\pi\) | ||||
0.183299 | + | 0.983057i | \(0.441322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.46090 | −0.473719 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.63595 | −0.146896 | ||||||||
\(323\) | −1.34435 | −0.0748017 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.54735 | 0.251854 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.0906 | −0.778021 | ||||||||
\(329\) | −9.54165 | −0.526048 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.2523 | 1.82771 | 0.913857 | − | 0.406037i | \(-0.133090\pi\) | ||||
0.913857 | + | 0.406037i | \(0.133090\pi\) | |||||||
\(332\) | 0.731789 | 0.0401621 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.3363 | −1.55049 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9653 | 0.924160 | 0.462080 | − | 0.886838i | \(-0.347103\pi\) | ||||
0.462080 | + | 0.886838i | \(0.347103\pi\) | |||||||
\(338\) | 4.93365 | 0.268355 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −52.3362 | −2.83416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9006 | 0.696567 | ||||||||
\(344\) | 17.4694 | 0.941888 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.9063 | −1.33897 | ||||||||
\(347\) | 20.1449 | 1.08144 | 0.540719 | − | 0.841203i | \(-0.318152\pi\) | ||||
0.540719 | + | 0.841203i | \(0.318152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.8420 | −1.59741 | −0.798703 | − | 0.601725i | \(-0.794480\pi\) | ||||
−0.798703 | + | 0.601725i | \(0.794480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.6589 | 0.568120 | ||||||||
\(353\) | −0.982924 | −0.0523157 | −0.0261579 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261579 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.99555 | −0.105764 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.1840 | 1.22531 | ||||||||
\(359\) | 33.4999 | 1.76806 | 0.884030 | − | 0.467431i | \(-0.154820\pi\) | ||||
0.884030 | + | 0.467431i | \(0.154820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0294 | −0.580495 | ||||||||
\(362\) | −5.24263 | −0.275546 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.27120 | −0.0666290 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.352799 | 0.0184160 | 0.00920798 | − | 0.999958i | \(-0.497069\pi\) | ||||
0.00920798 | + | 0.999958i | \(0.497069\pi\) | |||||||
\(368\) | −7.92300 | −0.413015 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.52062 | 0.338534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2811 | −1.25723 | −0.628614 | − | 0.777718i | \(-0.716377\pi\) | ||||
−0.628614 | + | 0.777718i | \(0.716377\pi\) | |||||||
\(374\) | 4.33093 | 0.223947 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.6540 | −1.27144 | ||||||||
\(377\) | 5.70802 | 0.293978 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.4446 | −1.87203 | −0.936017 | − | 0.351956i | \(-0.885517\pi\) | ||||
−0.936017 | + | 0.351956i | \(0.885517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.1058 | −1.18219 | ||||||||
\(383\) | −6.63250 | −0.338905 | −0.169453 | − | 0.985538i | \(-0.554200\pi\) | ||||
−0.169453 | + | 0.985538i | \(0.554200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.3627 | 1.08733 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.21891 | 0.214183 | ||||||||
\(389\) | −2.94097 | −0.149113 | −0.0745566 | − | 0.997217i | \(-0.523754\pi\) | ||||
−0.0745566 | + | 0.997217i | \(0.523754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.831862 | −0.0420690 | ||||||||
\(392\) | 15.4092 | 0.778282 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −36.2183 | −1.82465 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.44435 | −0.473998 | −0.236999 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.236999 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(398\) | −24.2771 | −1.21690 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.3968 | −1.21832 | −0.609159 | − | 0.793048i | \(-0.708493\pi\) | ||||
−0.609159 | + | 0.793048i | \(0.708493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.3078 | 1.75881 | ||||||||
\(404\) | 2.04181 | 0.101584 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.13718 | −0.106067 | ||||||||
\(407\) | 48.1481 | 2.38661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6073 | 0.672836 | 0.336418 | − | 0.941713i | \(-0.390784\pi\) | ||||
0.336418 | + | 0.941713i | \(0.390784\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.98673 | 0.147146 | ||||||||
\(413\) | 12.9582 | 0.637629 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.19085 | −0.352560 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.6779 | −1.25595 | ||||||||
\(419\) | −25.0654 | −1.22452 | −0.612262 | − | 0.790655i | \(-0.709740\pi\) | ||||
−0.612262 | + | 0.790655i | \(0.709740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.56078 | −0.271016 | −0.135508 | − | 0.990776i | \(-0.543267\pi\) | ||||
−0.135508 | + | 0.990776i | \(0.543267\pi\) | |||||||
\(422\) | −9.88192 | −0.481044 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.8482 | 0.818221 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0913 | −0.585139 | ||||||||
\(428\) | 4.26878 | 0.206339 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.2599 | −1.16856 | −0.584279 | − | 0.811553i | \(-0.698623\pi\) | ||||
−0.584279 | + | 0.811553i | \(0.698623\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.8459 | 1.86681 | 0.933407 | − | 0.358821i | \(-0.116821\pi\) | ||||
0.933407 | + | 0.358821i | \(0.116821\pi\) | |||||||
\(434\) | −13.2199 | −0.634574 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.896274 | 0.0429238 | ||||||||
\(437\) | 4.93207 | 0.235933 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.22879 | −0.440466 | −0.220233 | − | 0.975447i | \(-0.570682\pi\) | ||||
−0.220233 | + | 0.975447i | \(0.570682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.92179 | −0.138976 | ||||||||
\(443\) | 5.30591 | 0.252091 | 0.126046 | − | 0.992024i | \(-0.459771\pi\) | ||||
0.126046 | + | 0.992024i | \(0.459771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.3609 | 0.774710 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.29645 | −0.297479 | ||||||||
\(449\) | 22.2199 | 1.04862 | 0.524311 | − | 0.851527i | \(-0.324323\pi\) | ||||
0.524311 | + | 0.851527i | \(0.324323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.8719 | −1.54788 | ||||||||
\(452\) | 6.18324 | 0.290835 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.4286 | 0.489440 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.77157 | −0.316761 | −0.158380 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158380 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(458\) | 3.37072 | 0.157503 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.9340 | −1.58046 | −0.790231 | − | 0.612809i | \(-0.790040\pi\) | ||||
−0.790231 | + | 0.612809i | \(0.790040\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.8896 | −1.34262 | −0.671308 | − | 0.741179i | \(-0.734267\pi\) | ||||
−0.671308 | + | 0.741179i | \(0.734267\pi\) | |||||||
\(464\) | −6.42384 | −0.298219 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.3076 | 0.662786 | ||||||||
\(467\) | 31.2100 | 1.44423 | 0.722113 | − | 0.691776i | \(-0.243171\pi\) | ||||
0.722113 | + | 0.691776i | \(0.243171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.2174 | −0.517972 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 33.4817 | 1.54112 | ||||||||
\(473\) | 40.7544 | 1.87389 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.150205 | 0.00688464 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.12264 | 0.0513482 | ||||||||
\(479\) | 14.6580 | 0.669741 | 0.334870 | − | 0.942264i | \(-0.391307\pi\) | ||||
0.334870 | + | 0.942264i | \(0.391307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.4824 | −1.48107 | ||||||||
\(482\) | −6.42377 | −0.292595 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.85670 | 0.357123 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.55868 | 0.251888 | 0.125944 | − | 0.992037i | \(-0.459804\pi\) | ||||
0.125944 | + | 0.992037i | \(0.459804\pi\) | |||||||
\(488\) | −31.2419 | −1.41425 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4593 | 0.787925 | 0.393962 | − | 0.919127i | \(-0.371104\pi\) | ||||
0.393962 | + | 0.919127i | \(0.371104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.674459 | −0.0303761 | ||||||||
\(494\) | 17.3232 | 0.779407 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −39.7356 | −1.78418 | ||||||||
\(497\) | −5.38152 | −0.241394 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3254 | 0.730825 | 0.365412 | − | 0.930846i | \(-0.380928\pi\) | ||||
0.365412 | + | 0.930846i | \(0.380928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.9538 | 0.667420 | ||||||||
\(503\) | 16.7612 | 0.747345 | 0.373672 | − | 0.927561i | \(-0.378098\pi\) | ||||
0.373672 | + | 0.927561i | \(0.378098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.8890 | −0.706354 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.04472 | 0.0907196 | ||||||||
\(509\) | −8.35851 | −0.370485 | −0.185242 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185242 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.05248 | 0.179271 | ||||||||
\(512\) | −15.1330 | −0.668791 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.0584497 | −0.00257811 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.5154 | −2.52953 | ||||||||
\(518\) | 12.1620 | 0.534367 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 45.6262 | 1.99892 | 0.999460 | − | 0.0328599i | \(-0.0104615\pi\) | ||||
0.999460 | + | 0.0328599i | \(0.0104615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.6701 | −1.16620 | −0.583102 | − | 0.812399i | \(-0.698161\pi\) | ||||
−0.583102 | + | 0.812399i | \(0.698161\pi\) | |||||||
\(524\) | 2.32384 | 0.101518 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.7285 | 0.947406 | ||||||||
\(527\) | −4.17197 | −0.181734 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9481 | −0.867309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.890559 | −0.0386106 | ||||||||
\(533\) | 22.1765 | 0.960571 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −28.9839 | −1.25191 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −32.5974 | −1.40537 | ||||||||
\(539\) | 35.9481 | 1.54840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.225005 | −0.00967370 | −0.00483685 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483685 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(542\) | 9.48282 | 0.407322 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.849670 | 0.0364293 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.58474 | 0.367057 | 0.183529 | − | 0.983014i | \(-0.441248\pi\) | ||||
0.183529 | + | 0.983014i | \(0.441248\pi\) | |||||||
\(548\) | 2.49829 | 0.106722 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.99884 | 0.170356 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8718 | −0.632411 | ||||||||
\(554\) | −21.3820 | −0.908435 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.42762 | −0.230182 | ||||||||
\(557\) | 20.6736 | 0.875968 | 0.437984 | − | 0.898983i | \(-0.355693\pi\) | ||||
0.437984 | + | 0.898983i | \(0.355693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4943 | −1.16289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.787174 | 0.0332049 | ||||||||
\(563\) | −12.6162 | −0.531708 | −0.265854 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.48781 | 0.0625375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.9049 | −0.583439 | ||||||||
\(569\) | −10.9897 | −0.460714 | −0.230357 | − | 0.973106i | \(-0.573989\pi\) | ||||
−0.230357 | + | 0.973106i | \(0.573989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.276517 | 0.0115719 | 0.00578593 | − | 0.999983i | \(-0.498158\pi\) | ||||
0.00578593 | + | 0.999983i | \(0.498158\pi\) | |||||||
\(572\) | −7.66258 | −0.320389 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.30327 | −0.346572 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7460 | −0.655515 | −0.327757 | − | 0.944762i | \(-0.606293\pi\) | ||||
−0.327757 | + | 0.944762i | \(0.606293\pi\) | |||||||
\(578\) | −25.5390 | −1.06228 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.27826 | −0.0945180 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.3052 | 1.62785 | ||||||||
\(584\) | 10.4709 | 0.433291 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.19569 | −0.173322 | ||||||||
\(587\) | 11.3751 | 0.469501 | 0.234751 | − | 0.972056i | \(-0.424573\pi\) | ||||
0.234751 | + | 0.972056i | \(0.424573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.7354 | 1.01921 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 36.5559 | 1.50244 | ||||||||
\(593\) | 30.4617 | 1.25091 | 0.625457 | − | 0.780259i | \(-0.284913\pi\) | ||||
0.625457 | + | 0.780259i | \(0.284913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.905161 | −0.0370769 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.7193 | 0.438345 | ||||||||
\(599\) | −3.09493 | −0.126455 | −0.0632277 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632277 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.19481 | 0.375064 | 0.187532 | − | 0.982258i | \(-0.439951\pi\) | ||||
0.187532 | + | 0.982258i | \(0.439951\pi\) | |||||||
\(602\) | 10.2944 | 0.419567 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.68426 | 0.149911 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.9938 | 1.54212 | 0.771060 | − | 0.636762i | \(-0.219727\pi\) | ||||
0.771060 | + | 0.636762i | \(0.219727\pi\) | |||||||
\(608\) | −5.03766 | −0.204304 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.8019 | 1.56976 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.7188 | −0.998381 | −0.499191 | − | 0.866492i | \(-0.666369\pi\) | ||||
−0.499191 | + | 0.866492i | \(0.666369\pi\) | |||||||
\(614\) | 24.6570 | 0.995075 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.1575 | −0.610712 | ||||||||
\(617\) | −29.8302 | −1.20092 | −0.600460 | − | 0.799655i | \(-0.705016\pi\) | ||||
−0.600460 | + | 0.799655i | \(0.705016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.9427 | −0.841757 | −0.420878 | − | 0.907117i | \(-0.638278\pi\) | ||||
−0.420878 | + | 0.907117i | \(0.638278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.4867 | −0.500673 | ||||||||
\(623\) | 6.21268 | 0.248906 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 30.4618 | 1.21750 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.51920 | 0.0606226 | ||||||||
\(629\) | 3.83812 | 0.153036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1871 | 0.724017 | 0.362009 | − | 0.932175i | \(-0.382091\pi\) | ||||
0.362009 | + | 0.932175i | \(0.382091\pi\) | |||||||
\(632\) | −38.4261 | −1.52851 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.93813 | 0.394693 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.2519 | −0.960894 | ||||||||
\(638\) | −12.8826 | −0.510025 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.94506 | −0.155821 | −0.0779103 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779103 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1026 | 0.911077 | 0.455538 | − | 0.890216i | \(-0.349447\pi\) | ||||
0.455538 | + | 0.890216i | \(0.349447\pi\) | |||||||
\(644\) | −0.551063 | −0.0217149 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.04691 | −0.0805345 | ||||||||
\(647\) | 9.35622 | 0.367831 | 0.183916 | − | 0.982942i | \(-0.441123\pi\) | ||||
0.183916 | + | 0.982942i | \(0.441123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 78.1095 | 3.06607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.950655 | 0.0372305 | ||||||||
\(653\) | −2.29702 | −0.0898892 | −0.0449446 | − | 0.998989i | \(-0.514311\pi\) | ||||
−0.0449446 | + | 0.998989i | \(0.514311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.9576 | −0.974429 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.5281 | −0.566365 | ||||||||
\(659\) | 17.5619 | 0.684116 | 0.342058 | − | 0.939679i | \(-0.388876\pi\) | ||||
0.342058 | + | 0.939679i | \(0.388876\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.88170 | −0.267667 | −0.133834 | − | 0.991004i | \(-0.542729\pi\) | ||||
−0.133834 | + | 0.991004i | \(0.542729\pi\) | |||||||
\(662\) | 50.6300 | 1.96779 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.88664 | −0.228446 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47441 | 0.0958097 | ||||||||
\(668\) | −5.92390 | −0.229202 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −72.8842 | −2.81367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4307 | −0.479168 | −0.239584 | − | 0.970876i | \(-0.577011\pi\) | ||||
−0.239584 | + | 0.970876i | \(0.577011\pi\) | |||||||
\(674\) | 25.8314 | 0.994989 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.03141 | 0.0396697 | ||||||||
\(677\) | 6.61696 | 0.254310 | 0.127155 | − | 0.991883i | \(-0.459415\pi\) | ||||
0.127155 | + | 0.991883i | \(0.459415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1346 | −0.504060 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −79.6870 | −3.05137 | ||||||||
\(683\) | 18.6885 | 0.715097 | 0.357549 | − | 0.933895i | \(-0.383613\pi\) | ||||
0.357549 | + | 0.933895i | \(0.383613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.6424 | 0.749952 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.9423 | 1.17966 | ||||||||
\(689\) | −26.5166 | −1.01020 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.4352 | −0.701306 | −0.350653 | − | 0.936505i | \(-0.614040\pi\) | ||||
−0.350653 | + | 0.936505i | \(0.614040\pi\) | |||||||
\(692\) | −5.20684 | −0.197934 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.6727 | 1.16432 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.62038 | −0.0992538 | ||||||||
\(698\) | −45.4375 | −1.71983 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.9443 | −0.564437 | −0.282219 | − | 0.959350i | \(-0.591070\pi\) | ||||
−0.282219 | + | 0.959350i | \(0.591070\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.7561 | −0.858261 | ||||||||
\(704\) | −37.9539 | −1.43044 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.49660 | −0.0563253 | ||||||||
\(707\) | −6.35670 | −0.239068 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.4198 | 1.66822 | 0.834110 | − | 0.551598i | \(-0.185982\pi\) | ||||
0.834110 | + | 0.551598i | \(0.185982\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.0525 | 0.601594 | ||||||||
\(713\) | 15.3059 | 0.573209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.84678 | 0.181133 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 51.0070 | 1.90356 | ||||||||
\(719\) | 38.9409 | 1.45225 | 0.726125 | − | 0.687563i | \(-0.241319\pi\) | ||||
0.726125 | + | 0.687563i | \(0.241319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.29850 | −0.346294 | ||||||||
\(722\) | −16.7934 | −0.624984 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.09601 | −0.0407328 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.48415 | 0.0921320 | 0.0460660 | − | 0.998938i | \(-0.485332\pi\) | ||||
0.0460660 | + | 0.998938i | \(0.485332\pi\) | |||||||
\(728\) | 10.2258 | 0.378992 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.24873 | 0.120159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.7905 | −1.17421 | −0.587105 | − | 0.809511i | \(-0.699733\pi\) | ||||
−0.587105 | + | 0.809511i | \(0.699733\pi\) | |||||||
\(734\) | 0.537172 | 0.0198274 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.11722 | −0.114902 | ||||||||
\(737\) | −67.6166 | −2.49069 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.4392 | −1.19329 | −0.596647 | − | 0.802504i | \(-0.703501\pi\) | ||||
−0.596647 | + | 0.802504i | \(0.703501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.92829 | 0.364479 | ||||||||
\(743\) | 2.02921 | 0.0744447 | 0.0372223 | − | 0.999307i | \(-0.488149\pi\) | ||||
0.0372223 | + | 0.999307i | \(0.488149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −36.9704 | −1.35358 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.905410 | 0.0331051 | ||||||||
\(749\) | −13.2899 | −0.485602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8934 | −1.16381 | −0.581904 | − | 0.813257i | \(-0.697692\pi\) | ||||
−0.581904 | + | 0.813257i | \(0.697692\pi\) | |||||||
\(752\) | −43.6679 | −1.59241 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.69102 | 0.316508 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.2724 | 1.42738 | 0.713689 | − | 0.700463i | \(-0.247023\pi\) | ||||
0.713689 | + | 0.700463i | \(0.247023\pi\) | |||||||
\(758\) | −55.4905 | −2.01551 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.2422 | −0.516278 | −0.258139 | − | 0.966108i | \(-0.583109\pi\) | ||||
−0.258139 | + | 0.966108i | \(0.583109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.79034 | −0.101017 | ||||||||
\(764\) | −4.83042 | −0.174758 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.0987 | −0.364879 | ||||||||
\(767\) | −52.6954 | −1.90272 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.86409 | −0.247526 | −0.123763 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123763 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.46601 | 0.160735 | ||||||||
\(773\) | 8.46681 | 0.304530 | 0.152265 | − | 0.988340i | \(-0.451343\pi\) | ||||
0.152265 | + | 0.988340i | \(0.451343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −33.9377 | −1.21829 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.47792 | −0.160541 | ||||||||
\(779\) | 15.5361 | 0.556638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.4389 | −1.16075 | ||||||||
\(782\) | −1.26659 | −0.0452932 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.2932 | 0.974757 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9960 | −0.534551 | −0.267275 | − | 0.963620i | \(-0.586123\pi\) | ||||
−0.267275 | + | 0.963620i | \(0.586123\pi\) | |||||||
\(788\) | −7.57169 | −0.269730 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.2501 | −0.684455 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.1703 | 1.74609 | ||||||||
\(794\) | −14.3800 | −0.510326 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.07530 | −0.179889 | ||||||||
\(797\) | 10.9127 | 0.386549 | 0.193274 | − | 0.981145i | \(-0.438089\pi\) | ||||
0.193274 | + | 0.981145i | \(0.438089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.58483 | −0.162200 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.1465 | −1.31169 | ||||||||
\(803\) | 24.4277 | 0.862033 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 53.7597 | 1.89360 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.4246 | −0.577817 | ||||||||
\(809\) | −13.8729 | −0.487746 | −0.243873 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243873 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1036 | 0.460129 | 0.230065 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230065 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(812\) | −0.446793 | −0.0156793 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 73.3103 | 2.56953 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.2616 | −0.673878 | ||||||||
\(818\) | 20.7184 | 0.724403 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5589 | −0.543011 | −0.271505 | − | 0.962437i | \(-0.587521\pi\) | ||||
−0.271505 | + | 0.962437i | \(0.587521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.2205 | 1.57629 | 0.788144 | − | 0.615491i | \(-0.211042\pi\) | ||||
0.788144 | + | 0.615491i | \(0.211042\pi\) | |||||||
\(824\) | −24.0258 | −0.836978 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.7301 | 0.686497 | ||||||||
\(827\) | 25.6349 | 0.891411 | 0.445706 | − | 0.895180i | \(-0.352953\pi\) | ||||
0.445706 | + | 0.895180i | \(0.352953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6302 | 0.508129 | 0.254064 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254064 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.6050 | 0.887695 | ||||||||
\(833\) | 2.86560 | 0.0992872 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.36814 | −0.185661 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −38.1645 | −1.31837 | ||||||||
\(839\) | −37.4349 | −1.29240 | −0.646199 | − | 0.763169i | \(-0.723642\pi\) | ||||
−0.646199 | + | 0.763169i | \(0.723642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9938 | −0.930820 | ||||||||
\(842\) | −8.46684 | −0.291787 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.06588 | −0.0711106 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.4600 | −0.840457 | ||||||||
\(848\) | 29.8420 | 1.02478 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0811 | −0.482693 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.45661 | −0.152591 | −0.0762956 | − | 0.997085i | \(-0.524309\pi\) | ||||
−0.0762956 | + | 0.997085i | \(0.524309\pi\) | |||||||
\(854\) | −18.4102 | −0.629984 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −34.3388 | −1.17368 | ||||||||
\(857\) | −48.0738 | −1.64217 | −0.821084 | − | 0.570807i | \(-0.806630\pi\) | ||||
−0.821084 | + | 0.570807i | \(0.806630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.5317 | −1.38292 | −0.691461 | − | 0.722414i | \(-0.743033\pi\) | ||||
−0.691461 | + | 0.722414i | \(0.743033\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.9381 | −1.25812 | ||||||||
\(863\) | −7.99001 | −0.271983 | −0.135992 | − | 0.990710i | \(-0.543422\pi\) | ||||
−0.135992 | + | 0.990710i | \(0.543422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 59.1467 | 2.00989 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.76370 | −0.0938062 | ||||||||
\(869\) | −89.6444 | −3.04098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.6165 | 1.54566 | ||||||||
\(872\) | −7.20979 | −0.244154 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.50957 | 0.254015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.7432 | 1.03812 | 0.519062 | − | 0.854737i | \(-0.326281\pi\) | ||||
0.519062 | + | 0.854737i | \(0.326281\pi\) | |||||||
\(878\) | −14.0518 | −0.474224 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1508 | 1.18426 | 0.592130 | − | 0.805843i | \(-0.298287\pi\) | ||||
0.592130 | + | 0.805843i | \(0.298287\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.8185 | −1.20539 | −0.602694 | − | 0.797972i | \(-0.705906\pi\) | ||||
−0.602694 | + | 0.797972i | \(0.705906\pi\) | |||||||
\(884\) | −0.610821 | −0.0205441 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.07877 | 0.271412 | ||||||||
\(887\) | 30.3154 | 1.01789 | 0.508946 | − | 0.860798i | \(-0.330035\pi\) | ||||
0.508946 | + | 0.860798i | \(0.330035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.36575 | −0.213501 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.42035 | 0.114522 | ||||||||
\(893\) | 27.1833 | 0.909654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.1235 | −0.438426 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.8320 | 1.12899 | ||||||||
\(899\) | 12.4097 | 0.413888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.13321 | 0.104382 | ||||||||
\(902\) | −50.0507 | −1.66651 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.7390 | −1.65430 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.79755 | −0.225709 | −0.112854 | − | 0.993612i | \(-0.535999\pi\) | ||||
−0.112854 | + | 0.993612i | \(0.535999\pi\) | |||||||
\(908\) | 2.18018 | 0.0723517 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.3310 | 1.13744 | 0.568719 | − | 0.822532i | \(-0.307439\pi\) | ||||
0.568719 | + | 0.822532i | \(0.307439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7329 | −0.454494 | ||||||||
\(914\) | −10.3104 | −0.341037 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.704672 | 0.0232830 | ||||||||
\(917\) | −7.23475 | −0.238913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.72902 | 0.221970 | 0.110985 | − | 0.993822i | \(-0.464599\pi\) | ||||
0.110985 | + | 0.993822i | \(0.464599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −51.6679 | −1.70159 | ||||||||
\(923\) | 21.8844 | 0.720333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −43.9874 | −1.44551 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.52739 | −0.0829656 | ||||||||
\(929\) | 4.70020 | 0.154209 | 0.0771043 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771043 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.9900 | −0.556825 | ||||||||
\(932\) | 2.99110 | 0.0979768 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 47.5203 | 1.55491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.41847 | 0.0463395 | 0.0231698 | − | 0.999732i | \(-0.492624\pi\) | ||||
0.0231698 | + | 0.999732i | \(0.492624\pi\) | |||||||
\(938\) | −17.0796 | −0.557669 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.7929 | 1.59060 | 0.795302 | − | 0.606213i | \(-0.207312\pi\) | ||||
0.795302 | + | 0.606213i | \(0.207312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.61347 | 0.313058 | ||||||||
\(944\) | 59.3037 | 1.93017 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.0526 | 2.01751 | ||||||||
\(947\) | 38.1885 | 1.24096 | 0.620480 | − | 0.784222i | \(-0.286938\pi\) | ||||
0.620480 | + | 0.784222i | \(0.286938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.4798 | −0.534955 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.20828 | −0.0391604 | ||||||||
\(953\) | 8.25677 | 0.267463 | 0.133731 | − | 0.991018i | \(-0.457304\pi\) | ||||
0.133731 | + | 0.991018i | \(0.457304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.234695 | 0.00759057 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.3183 | 0.721070 | ||||||||
\(959\) | −7.77785 | −0.251160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.7623 | 1.47620 | ||||||||
\(962\) | −49.4577 | −1.59458 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.34293 | −0.0432530 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.3033 | 1.39254 | 0.696270 | − | 0.717780i | \(-0.254842\pi\) | ||||
0.696270 | + | 0.717780i | \(0.254842\pi\) | |||||||
\(968\) | −63.2007 | −2.03135 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1452 | 1.12786 | 0.563932 | − | 0.825821i | \(-0.309288\pi\) | ||||
0.563932 | + | 0.825821i | \(0.309288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.8976 | 0.541713 | ||||||||
\(974\) | 8.46364 | 0.271192 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −55.3365 | −1.77128 | ||||||||
\(977\) | −40.4411 | −1.29383 | −0.646913 | − | 0.762563i | \(-0.723941\pi\) | ||||
−0.646913 | + | 0.762563i | \(0.723941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.4490 | 1.19687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.5835 | 0.848312 | ||||||||
\(983\) | 58.9585 | 1.88048 | 0.940241 | − | 0.340509i | \(-0.110599\pi\) | ||||
0.940241 | + | 0.340509i | \(0.110599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.02693 | −0.0327042 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.62153 | 0.115216 | ||||||||
\(989\) | −11.9187 | −0.378994 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0145 | 0.349888 | 0.174944 | − | 0.984578i | \(-0.444026\pi\) | ||||
0.174944 | + | 0.984578i | \(0.444026\pi\) | |||||||
\(992\) | −15.6335 | −0.496365 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.19390 | −0.259895 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.8873 | 1.67496 | 0.837479 | − | 0.546469i | \(-0.184029\pi\) | ||||
0.837479 | + | 0.546469i | \(0.184029\pi\) | |||||||
\(998\) | 24.8570 | 0.786836 | ||||||||
\(999\) | 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 | 5625.2.a.u.1.7 | 8 | ||
3.2 | odd | 2 | 1875.2.a.o.1.2 | yes | 8 | ||
5.4 | even | 2 | 5625.2.a.bc.1.2 | 8 | |||
15.2 | even | 4 | 1875.2.b.g.1249.4 | 16 | |||
15.8 | even | 4 | 1875.2.b.g.1249.13 | 16 | |||
15.14 | odd | 2 | 1875.2.a.n.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.n.1.7 | ✓ | 8 | 15.14 | odd | 2 | ||
1875.2.a.o.1.2 | yes | 8 | 3.2 | odd | 2 | ||
1875.2.b.g.1249.4 | 16 | 15.2 | even | 4 | |||
1875.2.b.g.1249.13 | 16 | 15.8 | even | 4 | |||
5625.2.a.u.1.7 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.bc.1.2 | 8 | 5.4 | even | 2 |